Question 720582
Let {{{ d }}} = the number of dimes
Let {{{ q }}} = the number of quarters
given:
(1) {{{ 10d + 25q = 890 }}}  ( in cents )
(2) {{{ 10q + 25d =  860 }}}
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Rewrite the equations
(1) {{{ 2d + 5q = 178 }}}
(2) {{{ 5d + 2q = 172 }}}
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Multiply both sides of (1) by
{{{ 5 }}} and both sides of (2)
by {{{ 2 }}} then subtract (2) from (1)
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(1) {{{ 10d + 25q = 890 }}}
(2) {{{ -10d -4q = -344 }}}
{{{ 21q = 546 }}}
{{{ q = 26 }}}
and
(1) {{{ 2d + 5q = 178 }}}
(1) {{{ 2d + 5*26 = 178 }}} 
(1) {{{ 2d = 178 - 130 }}}
(1) {{{ 2d = 48 }}}
(1) {{{ d = 24 }}}
The number of dimes in the bank is 24
The number of quarters in the bank is 26
check:
(2) {{{ 10q + 25d =  860 }}}
(2) {{{ 10*26 + 25*24 = 860 }}}
(2) {{{ 260 + 600 = 860 }}}
(2) {{{ 860 = 860 }}}
OK