Question 1157579
Let {{{ d }}} = the number of dimes they had
Let {{{ q }}} = the number of quarters they had
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(1) {{{ d + q = 58 }}}
(2) {{{ 10d + 25q = 985 }}} ( in cents )
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(2) {{{ 2d + 5q = 197 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2d + 5q = 197 }}}
(1) {{{ -2d - 2q = -116 }}}
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{{{ 3q = 81 }}}
{{{ q = 27 }}}
and
(1) {{{ d + q = 58 }}}
(1) {{{ d + 27 = 58 }}}
(1) {{{ d = 31 }}}
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There are 31 dimes and 27 quarters
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check:
(2) {{{ 2d + 5q = 197 }}}
(2) {{{ 2*31 + 5*27 = 197 }}}
(2) {{{ 62 + 135 = 197 }}}
(2) {{{ 197 = 197 }}}
OK