Question 453329
Let {{{a}}} = number of nickels
Let {{{b}}} = number of dimes
given:
(1) {{{ a + b = 12 }}}
(2) {{{ 5a + 10b = 80 }}} (in cents)
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Multiply both sides of (1) by {{{5}}}
and subtract from (2)
(2) {{{ 5a + 10b = 80 }}}
(1) {{{ -5a - 5b = -60 }}}
{{{ 5b = 20 }}}
{{{ b = 4 }}}
and, since
(1) {{{ a + b = 12 }}}
(1) {{{ a + 4 = 12 }}}
{{{ a = 8 }}}
There are 4 dimes in the purse
check answer:
(2) {{{ 5a + 10b = 80 }}}
(2) {{{ 5*8 + 10*4 = 80 }}}
(2) {{{ 40 + 40 = 80 }}}
{{{ 80 = 80 }}}
OK