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Answer 1 · 2017-11-17T16:31:17

37 quarters and 45 dimes

Because dimes and quarter numbers are unknown, we can use variables.
let d be dime quantity and q be quarter quantity

1 dime = 10 cents 1 quarter = 25 cents

$d + q = 82$ ----82 coins in all

$0.10d+0.25q=13.75$ -----in terms of cents equaling total

Here is a system of equations. Lets use substitution-

First isolate a variable
$d=82-q$
Substitute
$0.10(82-q)+0.25q=13.75$
$8.2-0.1q+0.25q=13.75$

And solve!
$q=37$

plug this in to any equation you like

$d+37=82$
$d=45$