Question

Ben has 3.40 consisting of quaters and dimes. How many coins of each kind does he have if he has 22 coins?

Answer 1

8 quarters and 14 dimes

Explanation:

This situation has two unknowns - the total number of dimes and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

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`d+q=22` is an equation representing the total number of coins

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`0.10d+0.25q=3.40` is an equation representing the total value in money based on the number of coin. 0.10 and 0.25 come from the value of a dime and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get
`d=22-q`. We now substitute this for d in the second equation.

`0.10(22-q)+0.25q=3.40\\2.2-0.10q+0.25q=3.40\\2.2+0.15q=3.40`

After simplifying, we subtract 2.2 across and divide by the coefficient of q.

`2.2+0.15q=3.40\\0.15q=1.20\\q=8`

We now know of the 22 coins that 8 are quarters. To find the number of dimes, we subtract 8 from 22 to get 14 dimes.