Question 839263
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d + q = 76 }}}
(2) {{{ 10d + 25q = 1300 }}} ( in cents )
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Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 1300 }}}
(1) {{{ -10d - 10q = -760 }}}
{{{ 15q = 540 }}}
{{{ q = 36 }}}
and, since
(1) {{{ d + q = 76 }}}
(1) {{{ d + 36 = 76 }}}
(1) {{{ d = 40 }}}
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There are 40 dimes and 36 quarters
check:
(2) {{{ 10*40 + 25*36 = 1300 }}} 
(2) {{{ 400 + 900 = 1300 }}}
(2) {{{ 1300 = 1300 }}}
OK