After collecting coins for a month, you count them to see how much money you have. You determine that you have 12 fewer quarters than you have nickels, and you have twice as many dimes as you have quarters. Altogether, the dimes, nickels, and quarters add up to $10.60. How many of each coin do you have?

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oeerivona oeerivona · Answer 1 · 2020-11-07T08:56:17+01:00

Answer:

There are 20 quarters, 40 dimes, and 32 nickels

Step-by-step explanation:

The given parameters are;

The number of quarters = The number of nickels - 12

The number of dimes = 2 × The number of quarters

The sum of the nickels, dimes, and quarters = $10.60

Given that the worth of a nickel = 5 cents, The worth of a dime = 10 cents and the worth of a quarter = 25 cents, we have;

Let the number of nickels = X, we have;

The number of quarters = X - 12

The number of dimes = 2 × (X - 12)

X× 5 + (X - 12) × 25+ (2 × (X - 12)) × 10 = 1060

50·X - 540 = 1060

50·X = 1060 + 540 = 1600

X = 1600/50 = 32

X = 32

The number of nickels = X = 32

The number of nickels = 32

The number of quarters = X - 12 = 32 - 12 = 20

The number of quarters = 20

The number of dimes = 2 × (X - 12) = 2 × (32 - 12) = 40

The number of dimes = 40