Inaaya has a jar of coins containing only nickels, dimes, and quarters. A nickel is
worth 5 cents, a dime is worth 10 cents, a quarter is worth 25 cents, and a dollar
is worth 100 cents.
The ratio of the number of quarters to the number of dimes to the number of
nickels in the jar is 9 : 3 : 1. The total value of all the coins in the jar is $18.20.
How many coins does Inaaya have in her jar?

Answer:

91 total coins

63 quarters, 21 dimes, 7 nickels

Step-by-step explanation:

What I did first was did (9 * 0.25) + (3 * 0.10) + (1 * 0.05) to establish a formula.  Next, I did trial and error until I met the appropriate number, but since they needed to stay within a ratio, every time I increased the nickels by one, I needed to increase the dimes by 3 and the quarters by 9.  I eventually got to (63 * 0.25) + (21 * 0.10) + (7 * 0.05) = $18.20

A dollar is usually divided as nickels, dimes and quarters. The total number of coins Inaaya have in her jar is 91

Suppose the real measurements were "a" and "b"

Then their ratio will be formed as

[tex]\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}[/tex]

where [tex]x[/tex] is a common factor (not 1)

This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly cancelled from both the numerator and the denominator.

Thus, a = px, b = qx

For the given case, let Inaaya has got the number of coins per type as:

Thus, total number of coins she get = x + y + z

Since we know that: a Nickel = $0.05, a Dime = $0.10, and a Quarter = $0.25

Thus,

Total value of money = [tex]$0.05 \times x + 0.10 \times y + 0.25 \times z[/tex] (in dollars)

Since it is given that she has got total amount in dollars as $18.20, thus,

[tex]0.05x + 0.1y + 0.25z = 18.2\\[/tex]

Also, let the ratio given is by cancelling a factor F, then

as it is given that:

Number of quarter : Number of dime : Number of nickel = 9 : 3 : 1

Then, using the equation we got for x, y, and z, we get:

[tex]0.05x + 0.1y + 0.25z = 18.2\\\\0.05(F) + 0.1(3F) + 0.25(9F) = 18.2\\0.05F + 0.3F + 2.25F = 18.2\\2.6F = 18.2\\F = 18.2/2.6 = 7[/tex]

Thus, number of quarters = 9F = 9 times 7  = 63

Number of dimes = 3F = 3 times 7 = 21

Number of nickels = 1F = F  = 7

Total coins = 63 + 21 + 7 = 91

Thus, the total number of coins Inaaya have in her jar is 91

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