Question 1029975
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d + q = 41 }}}
(2) {{{ 10d + 25q = 680 }}} ( in cents )
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Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 680 }}}
(1) {{{ -10d - 10q = -410 }}}
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{{{ 15q= 270 }}}
{{{ q = 18 }}}
and
(1) {{{ d + 18 = 41 }}}
(1) {{{ d = 23 }}}
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There are 23 dimes and 18 quarters
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check:
(2) {{{ 10d + 25q = 680 }}}
(2) {{{ 10*23 + 25*18 = 680 }}}
(2) {{{ 230 + 450 = 680 }}}
(2) {{{ 680 = 680 }}}
OK