Question 621577
Let {{{ n }}} = number of nickels
Let {{{ q }}} = number of quarters
given:
(1) {{{ n + q  = 80 }}}
(2) {{{ 5n + 25q = 1460 }}} ( in cents )
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Multiply both sides of (1) by {{{5}}}
and subtract (1) from (2)
(2) {{{ 5n + 25q = 1460 }}}
(1) {{{ -5n - 5q  = -400 }}}
{{{ 20q = 1060 }}}
{{{ q = 53 }}}
and, since
(1) {{{ n + q  = 80 }}}
(1) {{{ n + 53  = 80 }}}
(1) {{{ n = 27 }}}
They have 27 nickels and 53 quarters
check:
(2) {{{ 5*27 + 25*53 = 1460 }}}
(2) {{{ 135 + 1325 = 1460 }}}
(2) {{{ 1460 = 1460 }}}
OK