Question 1132844
Let {{{ d }}} = the number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ 10d + 25q = 690 }}} ( in cents )
(2) {{{ 10q + 25d = 780 }}} ( in cents )
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Multiply both sides of (1) by {{{ 5 }}}
Multiply both sides of (2) by {{{ 2 }}}
Subtract (2) from (1)
(1) {{{ 50d + 125q = 3450 }}}
(2) {{{ -50d - 20q = -1560 }}}
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{{{ 105q = 1890 }}}
{{{ q = 18 }}}
and
(1) {{{ 10d + 25*18 = 690 }}}
(1) {{{ 10d = 690 - 450 }}}
(1) {{{ 10d = 240 }}}
(1) {{{ d = 24 }}}
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There are 24 dimes and 18 quarters
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check:
(2) {{{ 10q + 25d = 780 }}}
(2) {{{ 10*18 + 25*24 = 780 }}}
(2) {{{ 180 + 600 = 780 }}}
(2) {{{ 780 = 780 }}}
OK