I have two turtles. Today, the older turtle's age is $11$ times that of the younger turtle. In $24$ years, the older turtle's age will only be $7$ times that of the younger turtle. If both turtles survive until then, how many years from today will the older turtle's age be triple that of the younger turtle?

Answers

Answer 1

Answer:

Let $y$ be the younger turtle's age today. Then the older turtle's age today is $11y.$ So $24$ years from now, the younger turtle's age will be $y+24$ and the older turtle's age will be $11y+24.$ However, we know the older turtle's age will be $7$ times that of the younger turtle then, which tells us that

\[11y+24=7(y+24).\]Distributing, we get $11y+24=7y+168.$ Subtracting $7y+24$ from both sides of this equation, we get $4y=144,$ so $y=36.$

This is the younger turtle's age today, but that's not what we're looking for in this problem - we're looking for the number of years from today that the older turtle's age will be triple that of the younger turtle. Let $k$ be this number of years. Since the younger turtle's age today is $y=36$ and the older turtle's age today is $11 \cdot 36=396,$ it follows that $k$ years from now my turtles' ages will be $36+k$ and $396+k$ respectively. Since we want to know when the older turtle's age will be triple that of the younger turtle, we want to know for what $k$ this equation will be true:

\[3(36+k)=396+k.\]Distributing, we get $108+3k=396+k.$ Subtracting $k+108$ from both sides of this equation, we get $2k=288.$ Therefore, $k=\boxed{144}.$

Step-by-step explanation:

Answer 2

A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500

How to solve Algebra Word Problems?

Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;

(x/6) - (x/5) = 50

Multiply by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

Let the older turtle be represented x and the younger one be y.

Todays age,

Older turtle = 11y years

Younger turtle = y years

Also the equation form as;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 396 years

Age of younger turtle today = 36 years

Therefore,

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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Related Questions

The number of bacteria can be represented by the equation A(t)=200(.75)^t, wherr A(t) is the amount of bacteria in grams and t is the number of days. a. Is this function growth or decay? b. What percent is the bacteria decreasing by each day? c. How many grams of bacteria will there be in 1 week? d. After how many days will there be half the initial amount of bacteria left?

Answers

Answer:

Step-by-step explanation:

a. This is a decay function, since the final value (A) gets smaller and smaller as the days pass by.

b. The bacteria is decreasing by 75% per day exponentially.

c. In order to calculate the amount of bacteria in a week we simply substitute the variable t for 7 (7 days in a week) and solve for A

A = 200(0.75)^7

A = 26.7 bacteria after 1 week

d. In order to calculate this we need to substitute the variable A with 100 and solve for t

100 = 200(0.75)^t   ... divide both side by 200

0.5 = 0.75^t

[tex]\frac{ln(0.5)}{ln(0.75)}[/tex] = t

2.4 = t

It will be half the initial amount after 2.4 days.

6.5. Does Spending Measure Welfare? Suppose a community spends $1 million on salaries and equipment for its police department. Because it believes that citizens are now more law-abiding, the community decides to cut back on the number of police it employs. As a result, the community now spends $800,000 less on police officers. The crime rate remains the same.

a. What happens to measured GDP?

b. Does GDP accurately reflect welfare in this case?

Discuss the underlying issue that this example poses.

Answers

Answer:

(a) Measured GDP will decrease by $200,0000

(b) No

Step-by-step explanation:

(a) Gross Domestic Product (GDP) is the total value in monetary terms of al the goods produced in a geographic location.

There will be a $200,000 decrease in the value of the GDP of the community as a result of reduction in the community spending from $1 million to $800,000.

(b) Generally, GDP is not a true indicator of welfare, likewise in this case, GDP does not reflect the welfare of the community.

There's a decrease in the community spending from $1 million to $800,000 but there's an increase in the welfare of the community as a result of decrease in crime rate.

HELP ME PLEASE!
The graph below shows a line graphed through the points

Answers

Answer:

The answer is C.) y = 2x + 5

answers r
6 units
7 units
8 units
9 units

Answers

Answer:

9 units

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

Help needed quick. I attacked the picture plz look

Answers

Answer: 55.3 is the correct ans

area of parallelogram=b*h

=7*7.9

=55.3

PLEASE HELPLPPPpppppp

Answers

Answer:

40

Step-by-step explanation:

it could be 40 all I did was subtract 80 from 120 but ¡dk wasn't really good in geometry

6v^2-6v-660
Factor the polynomial completely

Answers

Answer:

[tex]6 (v-11) (v + 10 )[/tex]

Step-by-step explanation:

i dont have any

AnsweR 6(V-11)(V+10)

Step-by-step explanation:

step1: after factoring out 6 we have :6v^2-6v-660=6(v^2-v-110)

step 2:identify constants b and c. b+-1 and c=-110

step3:find out all pairs of -110.

-1,110    1,110

-2,55    2,-55

-5,22      5,-22

-10,11      10,-11

step4: place 10 and 11 into place holders

x^2-x-110=(x+-)(x+-)

x^2-x-110=(x+10)(x-11)

PLEASE HELP!
For what values of x are the following expressions equal to each other:
the trinomials 3x^2 - 4x +3 and x^2+x+1

Answers

Answer:

x = 0.5, 2

[or 1/2, 2 if you want in fractions)

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

x=2

X=1/2 or 0.5

Step-by-step explanation:

First of all , i transfer every thing that was in the right side to the left side of equation and put 0 instead of them , then factor the new equation out by grouping them .

Good luck , hope it was helpful .

multiple choice question pls help!

Answers

pretty sure it's 18

what is 500 times 10​

Answers

Answer:

500*10=5,000

hope this helps

Answer:

5,000

Step-by-step explanation:

please correct me if im wrong


(b) Write down the coordinates of the turning point of y = x^2 - 2x - 4

Answers

Answer: [tex](1,-5)[/tex]

Step-by-step explanation:

Given

Curve is

[tex]y=x^2-2x-4[/tex]

At the turning point of the curve, the slope will be zero.

Differentiate the curve

[tex]\Rightarrow y'=2x-2[/tex]

Substitute 0 for [tex]y'[/tex]

[tex]\Rightarrow 2x-2=0\\\Rightarrow x=1[/tex]

[tex]\therefore y=1^2-2\times 1-4=-5[/tex]

[tex](1,-5)[/tex] is the turning point

What is the volume of a square pyramid with a base area of 36 and a height of 9 cm?
o 36 cm
o 108 cm
o 18 cm
o 324 cm

Answers

Answer:

D (108)

Step-by-step explanation:

I did test

The volume of a square pyramid with a base area of 36 and a height of 9 cm is 108 cm. The correct option is B.

What is pyramid?

A pyramid is a polyhedron with triangular faces that meet at a common vertex and a polygonal base.

The name of the pyramid is determined by the shape of the base. A pyramid with a square base, for example, is called a square pyramid; a pyramid with a triangular base, a triangular pyramid; and so on.

The formula to find the volume of a square pyramid is given by:

V = (1/3) x base area x height

Substituting the given values, we get:

V = (1/3) x 36 x 9

V = 108

Thus, the correct option is B.

For more details regarding pyramid, visit:

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what is the diameter of the circle below? use 2.14 for pi

Answers

Answer:

4.8

Step-by-step explanation:

d = 4.8

The diameter is the WHOLE line for the circle and it's given

Can Someone help me please I don't understand

Answers

Answer: 55 Gallons.

Step-by-step explanation: you can trust me on this, and I promise it will be correct.

Can someone help???!!!

Answers

function a is a linear equation


If the line segment at right is subdivided
into equal parts, what is the length of
the marked portion of the line?
75

Answers

Answer:

50

Step-by-step explanation:

75 dived into 3 parts can also be written as 75/3. 75/3 is 25 making each part worth 25. 2 segments are included in the marked portion so its 50 or (25 + 25)

What is a W-2? ОА. A tax form given to me by my employer each tax year to show my earnings and taxes withheld. ов. A tax form I fill out when I get my job to show my employer how many deductions I will be claiming on my taxes. OC. The tax form I fill out when I have to do my taxes. D. A tax form used by my parents to claim me on their income tax.​

Answers

Answer:

A) A tax form given to me by my employer each tax year to show my earnings and taxes withheld.

9/3
Streak
8 20th
3970
If you save $800 in the bank with an interest rate of 4%, how much money will you
have at the end of 5 years?

Answers

Answer:

$960

Step-by-step explanation:

Given data

Principal=$800

rate= 4%

time= 5years

Applying the compound interest expression we have]

A=P(1+rt)

substitute

A=800(1+0.04*5)

A=800(1+0.2)

A=800*1.2

A=$960

y=−x+2 y=3x−4 ​ khan

Answers

Answer: 0

Step-by-step explanation:

2y -3x - 4 = 0

Subtract 2y from both sides of the equation.

-3x - 4 = -2y

Add 4 to both sides of the equation.

-3x = -2y + 4

Divide each term by -3 and simplify

Show BOTH distribution and FOIL to find the product of LaTeX: (3x - 2) and (2x + 6). also explain

Answers

Answer:

(3x-2)=1x (2x+6)=8x

Step-by-step explanation:

Dollhouse furnishing come in different sizes depending on the size of the doll house. Whyyy ratio of the size of the dollhouse item to the size of the larger item dollhouse piano: 1 3/4 in. High real piano: 3ft 6in. High

Answers

Answer:

1: 24

Step-by-step explanation:

The ratio = size of smaller object/size of larger object = Height of dollhouse piano, h/height of real piano, H

H = 3 ft 6 in = 12 in/ft × 3 ft + 6 in = 36 in + 6 in = 42 in

h = 1³/₄ in = 7/4 in

So ratio = h/H = 7/4 in ÷ 42 in = 7/4 in × 1/42 in = 1/4 × 1/6 = 1/24

So ratio = h/H = 1/24 ⇒ h:H = 1: 24

Which has the greater value, -4 or -5?

please step by step

Answers

Answer:

-5 is the greater value

Step-by-step explanation: because they are both negative but if the other one is positive and the other one is negative, the positive is the greater value.

what is the measure of angle 1 ? pls i need help ​

Answers

This is a chord, chord angle problem.

Angle 1 = (50 + 56)/2. This leads to 53 degrees.

Answer:

58

Step-by-step explanation:

(50 + 56)/2 = 116/2 = 58

Can someone explain this to me

Answers

Answer:

[tex]\huge\boxed{\sf tan \ 28 = x / 14}[/tex]

Step-by-step explanation:

Since opposite and adjacent is given, we will use tan as trigonometric ratio.

Hence,

opposite = x , adjacent = 14 and [tex]\theta[/tex] = 28

So,

[tex]\sf tan \theta = opposite / adjacent[/tex]

tan 28 = x / 14

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

write the ratio in simplest form

30/55​

Answers

Answer:

6:7

Step-by-step explanation:

Hope it helps

#CARRY ON LEARNING

6/11

The numerator and denominator can each be divided by five. Once the denominator has been divided by five, it is now prime. That is as far as you can go.

Angle
& angle
Fill in all the missing angles in the picture.
are a vertical angle pair.
& angle
are an alternate interior
Angle
pair
are an alternate
Angle & angle
exterior pair
Angle
& angle
are a linear angle pair.
29°
are a corresponding
Angle & angle
angle pair

Answers

Answer:

hope this helps

Step-by-step explanation:

Angle _1_and angle _4_ are vertical angle pairs.

Angle _4_ and angle _5_ are an alternate interior pair.

Angle _2_ and angle _6_ are alternate exterior pair.

Angle _1_ and angle _2_ are a linear angle pair.

Angle _2_ and angle _7_ are corresponding angle pair.

Please please can someone help me asap thank you

Answers

Answer:

Answers bellow

Step-by-step explanation:

FIGURE A

Decreasing by 1/4 =25%

Figure B

Increase by 1/5 = 20 %

Page 2

b The amount of sunny days this year is 75% of the amount of sunny days last year

c The amount of houses sold this month is 150 % amount of houses sold last month

d The runner's time to complete this marathon was 110% he needed to complete the last marathon(not sure about that one )( it's either 90 % or 110)

Find the radius of the button

Answers

radius is half of diameter
d=28
28/2=14

radius =14

Answer:

the radius is 14

Step-by-step explanation:

... ....ur welcome.........

since the diameter of it is 28 the radius is half of it

Gina bought a thumbdrive and 12 writting pads for $13y . Each writting pad cost$2 Find the cost of the thumbdrive​

Answers

Answer:

its 24 since each one cost 2$

1) Using the image to the right, which of the following pairs of lines are parallel? A. a||b B. c||d C. a||d D. a||c HELP PLEASE

Answers

Answer:

C

Step-by-step explanation:

Answer:

c 100 percent

Step-by-step explanation:

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