Question 403234
The way I do it is:
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
-------------------------
given:
(1) {{{d + q = 40}}}
(2) {{{10 d + 25q = 670}}} (in cents)
--------------------------
Multiply both sides of (1) by {{{10}}}, and
subtract (1) from (2)
(2) {{{10 d + 25q = 670}}}
(1) {{{-10d - 10q = -400}}}
{{{15q = 270}}}
{{{q = 18}}}
and, from (1),
{{{d + 18 = 40}}}
{{{d = 22}}}
There are 22 dimes and 18 quarters
check answer:
(2) {{{10 d + 25q = 670}}}
(2) {{{10 *22 + 25*18 = 670}}}
(2) {{{220 + 450 = 670}}}
{{{670 = 670}}}
OK