Question 857922
Let {{{ q }}} = number of quarters
Let {{{ n }}} = number of nickels
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(1) {{{ q + n = 80 }}}
(2) {{{ 25q + 5n = 1460 }}} ( in cents )
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Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 25q + 5n = 1460 }}} 
(1) {{{ -5q - 5n = -400 }}}
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{{{ 20q = 1060 }}}
{{{ q = 53 }}}
and, since
(1) {{{ q + n = 80 }}}
(1) {{{ n = 80 - 53 }}}
(1) {{{ n = 27 }}}
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They have 53 quarters and 27 nickels
check:
(2) {{{ 25q + 5n = 1460 }}} 
(2) {{{ 25*53 + 5*27 = 1460 }}} 
(2) {{{ 1325 + 135 = 1460 }}}
(2) {{{ 1460 = 1460 }}}
OK