Question 1055366
Let {{{ q }}} = number of quarters
Let {{{ d }}} = number of dimes
-------------------------------
(1) {{{ q + d = 26 }}}
(2) {{{ 25q + 10d = 470 }}} ( in cents )
------------------------------------
(2) {{{ 5q + 2d = 94 }}}
Multiply both sides of (1) by {{{ 2 }}} and
subtract (1) from (2)
------------------------------------
(2) {{{ 5q + 2d = 94 }}}
(1) {{{ -2q - 2d = -52 }}}
---------------------------
{{{ 3q = 42 }}}
{{{ q = 14 }}}
and
(1) {{{ 14 + d = 26 }}}
(1) {{{ d = 12 }}}
---------------------------
She used 14 quarters and 12 dimes
-----------------------------------
check:
(2) {{{ 25q + 10d = 470 }}} 
(2) {{{ 25*14 + 10*12  = 470 }}} 
(2) {{{ 350 + 120 = 470 }}}
(2) {{{ 470 = 470 }}}
OK