The required length of the right rectangular prism is 18 in whose volume is 540 cu. in
What is a rectangular prism?Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in form. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its form. A rectangular prism may be found in everyday objects like a geometry box, notebooks, diaries, and rooms.
Rectangular prism characteristics
There are 6 faces, 12 edges, and 8 vertices on a rectangular prism.The rectangular prism's top and bottom are always rectangles.It has three dimensions, or length, breadth, and height, much like a cuboid.opposing face pairs are identical or coincidentThe lateral sides of a right rectangular prism are rectangle-shaped.The lateral faces of an oblique rectangular prim are parallelograms.Its cross-section is rectangular in shape.It has a perfect cuboid appearance.There are two categories into which rectangular prisms can be divided. These are:
Right Rectangular PrismOblique Rectangular PrismA rectangular prism is a prism with rectangular bases. A right rectangular prism is a prism with six rectangle-shaped faces with angles that are all right angles.
Vertices of a rectangular prism = 8
Edges of a rectangular prism = 12
Faces of a rectangular prism= 6 (including bases)
total volume of the prism = 540 cubic inches.
Width = 6 in
Height = 5 in
We know volume is length * breadth* height
⇒ 540 = 5*6* length
⇒length = 18 in
The required length of the right rectangular prism is 18 in.
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if a:3=12:a, calculate the positive of a
When a:3=12:a, then the positive of a will be 6.
Given, the following quadratic equation
a : 3 = 12 : a
That is,
a/3 = 12/a
By cross- multiplication of the values, we will get
a * a = 12 *3
a ^ 2 = 36
From the above equation, we calculate the square root for the value a.
Therefore, we get the square root of,
a ^ 2 = 36
a = 6 ( as the square root of 36 is 6)
So, we can say that when a : 3 = 12: a the positive of a will be 6
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The points in the table lie on a line. Find the slope of the line.
x: 1, 3, 5, 7
y: 2, 10, 18, 26
Answer:
Step-by-step explanation:
(1, 2), (3, 10)
(10 - 2)/(3 - 1) = 8/2 = 4
m = 4
Help me solve this two column proof!
The two column proof is written as follows
Statement Reason
AD ≅ BD ≅ CD given
ΔADB and ΔCDB are isosceles Base angles are equal
< A = < C = < ABD = < CBD = x Definition of isosceles triangle.
< ABC = < ABD + < CBD Adjacent angles
< ABC = x + x = 2x Substitution property of equality
< ABC + < A + < C = 180 Sum of angels of a triangle
2x + x + x = 180 Substitution property of equality
4x = 180 Addition property of equality
x = 45 degrees Division property of equality
< ABC = 2x = 2 * 45 Substitution property of equality
< ABC = 90 Definition of right triangle
What is a right triangle?A triangle is said to be a right triangle if one of the angles is 90 degrees. Right angles are angles that are 90 degrees.
The proof required to proof that < B is 90
With the isosceles triangle giving and the equal sides the equation is written as
4x = 180
x = 45
< B has 2x (< ABD + < CBD) these are adjacent angles
< B = 2 * 45
< B = 90
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Rory is writing an introduction paragraph for an argumentative essay about the treatment of egg-laying chickens. Which of the following is an effective
claim?
O Chickens raised for-eggs should be allowed to roam free.
OI like knowing that chickens are descended from dinosaurs, and that their egg colors are based on genetics and feather colors.
O It's important to note that chickens have great memories, dream when they sleep, and can recognize over 100 faces.
OWe should respect chickens because they can communicate with other chickens through over 30 different sounds, including purring when they're
happy.
An effective claim in the essay is that; Chickens raised for-eggs should be allowed to roam free. Option A
What is an argumentative essay?The entire point of an argumentative essay is that the essay helps us to be able to bee able to make a point. It is the kind of essay in which we may be able to communicate our perspective about a matter.
In the argumentative essay, there could be a claim which is the main point that the essay is trying to address. The claim would thus provide the kernel of the essay. It is the point that the author wants to pass across to the readers.
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Answer: A: Chickens raised for eggs should be allowed to roam free.
If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination.
Answer:
11 days
Step-by-step explanation:
y=24x+61
y=20x+105
(don't think I can solve this with elimination because there is no coefficient with a y-value.)
When looking for the interception you look for the point where both lines intercept. I graphed both equations online and looked for the point where they intercept, which is (11,325) meaning that in 11 days, both places will cost 325 dollars when you rent a car.
( I also looked for a calculator online that is especially used to find the interception between two points and it gave the same point, if wrong...I'm sorry)
Over which interval is this function continually decreasing? f(x) = |4(x - 1)| + 2
The interval at which the function f(x) = |4(x - 1)| + 2 is decreasing is (- ∞, 1).
What is an absolute value function?We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.
In piecewise terms | x | = x for x ≥ 0 and | x | = - x for x < 0.
We know in an absolute value function y = |x - h| + k, the vertex is (h, k) and it changes its direction from here.
Given, f(x) = |4(x - 1)| + 2 has a vertex at (1, 2).
Therefore the interval where the function is continuously decreasing is
( - ∞, 1).
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Two trains leave stations 480 miles apart at the same time and travel toward each other. One train travels at 90 miles per hour while the other travels at 110 miles per hour. How long will it take for the two trains to meet?
It will take 2 hours 24 minutes time to two trains to meet.
Let a train starts from A towards to B with velocity v1 = 90 miles/hour
and another train starts it's journey from B towars A with velocity v2 = 110 miles/hour
Let after time t hour they meet at C.
Hence, we get AC + CB = AB
⇒ v1t + v2t = 480
⇒ (v1 + v2) t = 480
⇒ (90 + 110) t = 480
⇒ t = 480/200 = 48/20 = 12/5 hours
∴ t = [tex]2\frac{2}{5}[/tex] hours
= 2 hour (2/5 × 60) mins
∴ t = 2 hours 24 minutes time
So, after 2 hours 24 minutes time they meet each otherv at C, where AC = v1t = 90 × 12/5 = 216 miles.
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Sarah has a solid wooden cube with a length of centimeter. From each of its 8 corners, she cuts out a smaller cube with a length of centimeter. What is the volume of the block after cutting out the smaller cubes?.
Therefore ,the volume of the block after cutting out the smaller cubes is (8/25 cm^2)
What is volume ?Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.
Volumes vary depending on the shape. We have examined different three-dimensional objects and shapes in geometry, including cubes, cuboids, cylinders, cones, and more. We will learn how to calculate the volume for each of these shapes.
Here,
volume = (8/25 cm2) represents the block's volume after the smaller cubes have been removed.
First, we must determine the volume of a cube with four or five centimeter sides, which is:
V = (4/5 cm)^2 = (16/25 cm^2)
The volume of each of the eight smaller cubes that was removed must now be subtracted.
v = (1/5 cm)^2 = (1/25 cm^2)
After the smaller cubes are removed, the block's volume is:
V - 8v = (16/25 cm^2) - 8*(1/25 cm^2) = (8/25 cm^2)
Therefore ,the volume of the block after cutting out the smaller cubes is (8/25 cm^2)
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Complete the table below to represent the function: f(x)=x+4
Answer:
x 0 1 2 3 4
f(x) 4 5 6 7 8
Step-by-step explanation:
f(x) = x + 4
f(0) = 0 + 4 = 4
f(1) = 1 + 4 = 5
f(2) = 2 + 4 = 6
f(3) = 3 + 4 = 7
f(4) = 4 + 4 = 8
x 0 1 2 3 4
f(x) 4 5 6 7 8
Add. Write the answer in standard form (6-1)+(7+3t)
Answer:
Step-by-step explanation:
12 + 3t
Can you help me thank you so so much Really having trouble in math
Answer:
Step-by-step explanation:
the answer is A
Answer:
A.) [tex]\frac{-343}{27}[/tex]
Step-by-step explanation:
Looking at the available answers, I'm assuming the expression is [tex](-2-\frac{1}{3})^3[/tex].
So,
[tex](-2-\frac{1}{3})^3\\(-\frac{6}{3}-\frac{1}{3})^3\\(\frac{-7}{3})^3[/tex]
Use the exponent rule that states [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex]
So,
[tex](\frac{-7}{3})^3\\\frac{(-7)^3}{3^3}\\\frac{-343}{27}[/tex]
Triangle ABC is shown in the xy-coordinate plane. The triangle will be translated 2 units down and 3 units right to create triangle A'B'C'. Indicate whether each of the listed parts of the image will or will not be the same as the corresponding part in the preimage (triangle ABC) by selecting the appropriate box in the table.
The coordinates of A' and C' will not be the same. The perimeter and area of ΔA'B'C' will be the same. The measure of ∠B' and the slope of A'C' will be the same.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the given translation,
2 units down and 3 units right
The coordinate will change as,(x,y) → (x+3,y-2) so it will change.
The transformation consists only of linear transformation no rotation exists thus area and perimeter will remain the same.
The slope and angle are unchanged irrespective of any transformation.
Hence "A' and C' will not have the same coordinates. The boundaries and surface area of ΔA'B'C' will be identical. The slope of A'C' and the measure of ∠B will be equal.".
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7) Skyler buys 8 T-shirts and 5 hats for $220. The next week, he buys 5 T-shirts and 1 had for $112. How
much does each T-shirt and each hat cost? Write a system of equations that can be used to solve the problem.
Step-by-step explanation:
As given in question that Skyler buys 8 T-shirts and 5 hats for $220.
The next day, he buys 5 T-shirts and 1 hat for $112.
We have to find the cost of T-shirt and hat each.
Let the cost of T-shirt and hat is x and y respectively.
According to the question,
8x + 5y = 220 ............(i)
5x + 1y = 112 ............(ii)
Multiply by 5 in eq. (ii)
25x + 5y = 560 ............(iii)
Now subtract eq. (iii) - eq. (i)
25x + 5y = 560
- 8x + 5y = 220
17x = 340
[tex]x = \frac{340}{17}[/tex]
∴ x = 20
Put the value of x in eq. (ii)
5 x 20 + y = 112
100 + y = 112
y = 112 - 100
∴ y = 12
Hence the cost of each T-shirt and each hat is $20 and $12 respectively.Patrick borrows $1400 from a bank with 10% simple interest each year. How much will patrick need to pay back in total in 2 years?.
Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280.
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Given data ,
Let the principal amount be = A
The value of A = $ 1400
Let the rate of interest be = r
The value of r = 10 %
Let the number of years = T
The value of T = 2 years
Now , the simple interest is calculated by the formula
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Substituting the values in the equation , we get
Simple Interest = ( 1400 x 10 x 2 ) / 100
Simple Interest = 14 x 20
Simple Interest = $ 280
Therefore , the simple interest in 2 years is $ 280
And , the total amount Patrick has to give back to the bank is given by the formula
Amount in 2 years = Principal + Interest
Amount in 2 years = 1400 + 280
Amount in 2 years = $ 1680
Therefore , the amount in 2 years is $ 1680
Hence , Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280
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If a boundary line is dashed, what does that mean about the ordered pairs that lie along that line?
The ordered pairs are never part of the solutions of the inequality.
The ordered pairs are sometimes part of the solutions of the inequality.
The ordered pairs are occasionally part of the solutions of the inequality.
The ordered pairs are always part of the solutions of the inequality.
If a boundary line is dashed, The ordered pairs are never part of the solutions of the inequality
What is inequality in math?
Inequality, is a mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Solid line and dashed line in inequality
A region on one side of a line can be used to graphically show an inequality.
For the purpose of indicating that a line is not a part of the region, inequality plots that employ the < or > symbols have a dashed line.
Plotting a solid line indicates that an inequality that uses the symbol ≤ or ≥ is included in the region.
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x-5/2 + x-1/8 = x-3/4 +x-4/3 GIVING BRAINLIEST!
Answer:
There are no values of x
that make the equation true.
No solution
Step-by-step explanation:
Indicate whether the measures 4. 35, 5. 8, and 7. 25 can be the side lengths of a triangle. If they can, classify the triangle. PLEASE HELP!!
yes; right
yes; obtuse
yes; acute
no
Classification of given triangle is right angle triangle.
Let's suppose a, b and c are the sides of a triangle.
then we know that sum of 2 sides is always greater than third side.
a + b>c
b + c>a
c + a>b
a = 4.35, b = 5.8 , c = 7.25
a + b>c 4.35+5.8 = 10.15>7.25
b + c>a 5.8 + 7.25 = 13.05>4.35
c + a>b 7.25+4.35 = 11.60>5.8
So now we can say given side lengths are representing sides of a triangle.
It generalizes the Pythagorean Theorem, which states that for a right-angled triangle square of the hypotenuse is equal to the sum of squares of the base and height of the triangle, which is [tex]c^2 = a^2 + b^2[/tex]
Similarly, It can be observed that
For acute-angled triangle
[tex]c^2 < a^2 + b^2[/tex]
For Obtuse-angled triangle
[tex]c^2 > a^2 + b^2[/tex]
[tex]a^2 + b^2[/tex] = 18.9225 + 33.64 = 52.5625
[tex]c^2[/tex] = 52.5625
clearly we can see that [tex]a^2+b^2 = c^2[/tex]
So given triangle is Right-angled triangle.
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HURRY I GOT 24 HOURS FOR THIS PLEASE HURRY!!!!!!
The area of the triangle below is 25/24
square inches. What is the length of the base? Express your answer as a fraction in simplest form.
Answer:
Base is 5/2
Step-by-step explanation:
lets say that 2x = the base.
25/24 = 2( [tex]\frac{1}{2}[/tex]([tex]\frac{5}{6}[/tex])x)
[tex]\frac{25}{24}[/tex] = 2( [tex]\frac{5}{12}[/tex]x)
[tex]\frac{25}{24}[/tex] = [tex]\frac{5}{6}[/tex]x
[tex]\frac{25}{24}[/tex] times [tex]\frac{6}{5}[/tex]= x
5/4 =x
2x = 10/4
2x = 5/2
Write an equation howing the relationhip. Ue `E` to repreent energy and `d` to repreent the number of day
Equation for representing energy to the number of days E = P*( 1/d / 1000 )
This formula of energy is used to calculate the use of energy for a given period in a day . The consumption of energy is measured by multiplying the number of power units consumed in a given period.
E = P*(1/d/1000); where E = energy measured in Joules or kilowatt-hours (kWh), P = power units in watts, and d = time over which the power or energy was consumed in a day
Thus, whenever someone asks you how to calculate power consumption, you can calculate and answer using the above equation.
Energy consumption can be widely classified based on several factors such as worldwide energy consumption, its impact on the environment, etc.
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Please help me solve!
Answer:
81.5%
Step-by-step explanation:
Note that 90 is 2 standard deviations away from 144, which accounted for 47.5% area
171 8 is 1 standard deviations away from the mean is which is 34% area.
So the total area is 81.5%
Which of the correlation values represent a perfect linear relationship between x and y?
A) .05
B) 1
C) 100
D) -1
E) 0
The correlation values for the perfect linear relationship is option (b) 1 and (d) -1.
Correlation:
Correlation refers the measure that determines the degree to which the movement of two different variables is associated.
Given,
Here we need to find the perfect correlation values that represent the perfect linear relationship between x and y.
Here we know that the perfect linear relationship is indicated by a correlation with a magnitude of 1.
Then the sign of the correlation coefficient is the sign of the slope of the line describing the relationship. And it may be positive or negative.
Therefore, the value -1 and 1 are the perfect values for this one.
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due a cupple days ago pls help meee
Answer:
(0, 2 )
Step-by-step explanation:
If the dilatation is centred at the origin then the original coordinates are multiplied by the scale factor , that is
B (0, 4 ) → ( [tex]\frac{1}{2}[/tex] (0), [tex]\frac{1}{2}[/tex] (4) ) → (0, 2 )
In one corner of the drawing room a flower basket is kept inside the glass lies on the table the basket is designed in such a way that every one please to see it
A cylindrical vase with a curved surface area of 6.79 square metres will cost Rs. 8.14 to paint.
What is curved surface area?The area with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area. Curved surface area is the amount of space left over after subtracting the cylinder's total circular area. The formula for curved surface area is 2 * pi * r * h.
Here,
We have to calculate the curved surface area of glass in which the flower basket is placed.
Glass is cylindrical,
Height of cylinder = 180cm = 1.8m
Radius of cylinder = 60cm = 0.6m
The curved surface area of the cylinder = 2πrh
The curved surface area of the cylinder = 2*22/7*0.6*1.8
The curved surface area of the cylinder = 6.78584 m²
Cost of painting the glass per m² = Rs. 1.2
Cost of painting 6.78584= 6.78584*1.2
Cost of painting 6.78584= Rs. 8.143
The cost of painting an cylindrical vase of curved surface area 6.79 m² will be Rs. 8.14.
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a confidence interval for a proportion ranges from 0.45 to 0.74. what is the margin of error for this confidence interval?
The margin of error for this confidence interval is 0.145.
Given :
a confidence interval for a proportion ranges from 0.45 to 0.74.
Confidence interval :
A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times
Margin of error :
Margin of error, also called confidence interval, tells you how much you can expect your survey results to reflect the views from the overall population.
Length of confidence interval = 0.74 - 0.45
= 0.29
we know that,
Margin of error = 1/2 * length of confidence interval.
= 1/2 * 0.29
= 0.29/2
= 0.145
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What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is wider than one other.
Confidence interval:
In statistics, confidence interval means the probability that a population parameter will fall between two set values.
Given,
Here we need to find the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean.
According to the given question, the given confidence interval values are 90% and 95 %.
When we convert this percentage value into decimal, then we get the value as,
90% = 0.9
95% = 0.95
Here a 95 percent confidence interval, you have a 5 percent chance of being wrong.
And with a 90 percent confidence interval, you have a 10 percent chance of being wrong.
Therefore, 90 percent confidence interval would be wider than a 95 percent confidence interval.
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The perimeter of a rectangle is 66cm.
Its longest side has a length of 17cm.
State the length of the shortest side.
[tex]{ \red{\boxed{ \tt{Step-by-step-explaination}}}}[/tex]
Perimeter of a rectangle : [tex]{ \purple{ \tt{2(l+b)}}}[/tex]
length = [tex]{ \red{ \tt{17cm}}}[/tex]
breadth= [tex]{ \red{ \tt{?}}}[/tex]
now,
according to the rule.
perimeter = 2(l+b)
66 = 2(17+b)
66 = 34 + 2b
66 - 34 = 2b
32 = 2b
32/2 = b
16 cm = b
hence b = [tex]{ \pink{ \sf{16cm}}}[/tex]
Julian is older than Nachelle. Their ages are consecutive odd integers. Find Julian's
age if the sum of the square of Julian's age and 2 times Nachelle's age is 139.
The age of Nachelle would be 5 years and the age of Julian would be 7 years.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Let's suppose the age of Nachelle is 'x' years then Julian's age would be 'x+2'.
x² + [2(x + 2)]² = 139
x² + 4x² + 8x + 16 = 139
5x² + 8x - 123 = 0
Simplifying this, we get
x = 4.22 and x = -5.82
Age cannot be a negative number so
x ≈ 5.
x + 2 = 7 years
Hence the age of Nachelle would be 5 years and the age of Julian would be 7 years.
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What is the LCM of 10, 20 and 35
What is the lcm
Dominic is a server at a restaurant. Each dish at the restaurant costs $8. A sales tax of 8% is charged. The total bill amount includes the sales tax of the meal. Dominic earns tips left by customers. The amount of money tipped can be represented by a percentage of the total bill. Order the tip amounts from least to greatest tip, in dollars. 4 dishes 20% tip 6 dishes 14% tip 7 dishes 11% tip
Answer: To find the tip amount in dollars for each order, you need to multiply the total bill amount by the tip percentage.
For the first order of 4 dishes, the total bill amount is $8 per dish * 4 dishes = $<<8*4=32>>32.
The tip amount is $32 * 20% = $6.40.
For the second order of 6 dishes, the total bill amount is $8 per dish * 6 dishes = $<<8*6=48>>48.
The tip amount is $48 * 14% = $6.72.
For the third order of 7 dishes, the total bill amount is $8 per dish * 7 dishes = $<<8*7=56>>56.
The tip amount is $56 * 11% = $6.16.
So, the tip amounts from least to greatest are $6.16, $6.40, and $6.72.
Ann has 30% less money than mary, and jessica has 70% more money than mary. If the three of them have a total of $102, how much money does each girl have individually?.
If Ann has 30% less money than mary, and jessica has 70% more money than mary and If the three of them have a total of $102, then Ann has $50.7, Mary has $51 and Jessica has $51.7
What is meant by percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It can be stated as a decimal or a fraction and is frequently represented by the sign "%". 50%, for instance, can be written as 0.5 or 1/2. A component or proportion of an entire is represented using percentages. For instance, if a student receives a 75% on an exam, it indicates that they correctly answered 75 out of 100 questions individually. Percentages are often used in everyday life to represent changes such as a rise or fall in pricing, an increase or reduction in population, or a growth or drop in sales. Percentages may be determined in mathematics using a variety of formulae and ideas including proportions, ratios, and decimals.
How to solve?
Ann has 30/100 * $x = $0.3x less money than Mary
Jessica has 70/100 * $x = $0.7x more money than Mary
Mary, Ann and Jessica have a total of $102
Mary + Ann + Jessica = $102
Mary + (Mary - $0.3x) + (Mary + $0.7x) = $102
3Mary = $102 + $0.3x + $0.7x
3Mary = $102 + $1x
3Mary = $102 + $x
3Mary - $x = $102
2Mary = $102
Mary = $102/2 = $51
Ann = Mary - $0.3x = $51 - $0.3x = $50.7
Jessica = Mary + $0.7x = $51 + $0.7x = $51.7
Ann has $50.7, Mary has $51 and Jessica has $51.7.
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If Ann has 30% less money than mary, and jessica has 70% more money than mary and If the three of them have a total of $102, then Ann has $50.7, Mary has $51 and Jessica has $51.7
What is meant by percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It can be stated as a decimal or a fraction and is frequently represented by the sign "%". 50%, for instance, can be written as 0.5 or 1/2. A component or proportion of an entire is represented using percentages. For instance, if a student receives a 75% on an exam, it indicates that they correctly answered 75 out of 100 questions individually. Percentages are often used in everyday life to represent changes such as a rise or fall in pricing, an increase or reduction in population, or a growth or drop in sales. Percentages may be determined in mathematics using a variety of formulae and ideas including proportions, ratios, and decimals.
Ann has 30/100 * $x = $0.3x less money than Mary
Jessica has 70/100 * $x = $0.7x more money than Mary
Mary, Ann and Jessica have a total of $102
Mary + Ann + Jessica = $102
Mary + (Mary - $0.3x) + (Mary + $0.7x) = $102
3Mary = $102 + $0.3x + $0.7x
3Mary = $102 + $1x
3Mary = $102 + $x
3Mary - $x = $102
2Mary = $102
Mary = $102/2 = $51
Ann = Mary - $0.3x = $51 - $0.3x = $50.7
Jessica = Mary + $0.7x = $51 + $0.7x = $51.7
Ann has $50.7, Mary has $51 and Jessica has $51.7.
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