Question 409124
Let {{{q}}} = number of quarters
Let {{{d}}} = number of dimes
given:
(1) {{{25q + 10d = 945}}} (in cents)
(2) {{{q + d = 60}}}
Multiply both sides of (2) by {{{10}}}
and subtract from (1)
(1) {{{25q + 10d = 945}}} 
(2) {{{-10q - 10d = -600}}}
{{{15q = 345}}}
{{{q = 23}}}
and, since
(2) {{{q + d = 60}}}
{{{d = 60 - 23}}}
{{{d = 37}}}
There are 37 dimes and 23 quarters
check answer:
(1) {{{25q + 10d = 945}}}
(1) {{{25*23 + 10*37 = 945}}}
{{{575 + 370 = 945}}}
{{{945 = 945}}}
OK