Question 519446
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
given:
(1) {{{ d = q - 5 }}}
(2) {{{ 10d + 25q = 3170 }}} ( in cents)
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(2) {{{ 2d + 5q = 634 }}}
and
(1) {{{ -d + q = 5 }}}
(1) {{{ -2d + 2q = 10 }}}
Add the equations
(2) {{{ 2d + 5q = 634 }}}
(1) {{{ -2d + 2q = 10 }}}
{{{ 7q = 644 }}}
{{{ q = 92 }}}
and
(1) {{{ d = q - 5 }}}
(1) {{{ d = 92 - 5 }}}
(1) {{{ d = 87 }}}
He has 87 dimes and 92 quarters
check:
(2) {{{ 10*87 + 25*92 = 3170 }}} 
(2) {{{ 870 + 2300 = 3170 }}}
(2) {{{ 3170 = 3170 }}}
OK