Question 397281
Le {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
(1) {{{d + q = 27}}}
(2) {{{10d + 25q = 540}}} (in cents)
Multiply both sides of (1) by {{{10}}},
and subtract (1) from (2)
(2) {{{10d + 25q = 540}}}
(1) {{{-10d - 10q = -270}}}
{{{15q = 270}}}
{{{q = 18}}}
and, since,
{{{d + 18 = 27}}}
{{{d = 9}}}
There are 9 dimes and 18 quarters
check answer:
(2) {{{10d + 25q = 540}}}
{{{10*9 + 25*18 = 540}}}
{{{90 + 450 = 540}}}
{{{540 = 540}}}
OK