When Jon went running in the park, he found 9 coins worth a total of $1.80. The coins were quarters and dimes. How many of each did he find?

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Answer 1 · 2016-12-16T14:25:19

Jon found 6 quarters and 3 dimes.

First, let's call the number of dimes Jon found $d$ and the number of quarters Jon found $q$

We can now write the following equation:
$d + q = 9$

And, because dimes are worth $0.10 and quarters are worth $0.25 we can write:

$0.1d + 0.25q = 1.80$

Solving the first equation for $d$ gives:

$d + q - q = 9 - q$

$d + 0 = 9 - q$

$d = 9 - q$

We can now substitute $9 - q$ for $d$ in the second equation and solve for $q$ :

$0.1(9 - q) + 0.25q = 1.80$

$0.9 - 0.1q + 0.25q = 1.80$

$0.9 + 0.15q = 1.80$

$0.9 - 0.9 + 0.15q = 1.80 - 0.9$

$0 + 0.15q = 0.9$

$0.15q = 0.9$

$(0.15q)/0.15 = 0.9/0.15$

$q = 6$

We can now substitute $6$ for $q$ in solution to the first equation and calculate $d$ :

$d = 9 - 6$

$d = 3$