Question 271339
Let {{{n}}} = number of nickels
Let {{{d}}} = number of dimes
given:
(1) {{{n + d = 30}}}
(2) {{{5n + 10d = 210}}} (in cents)
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Multiply both sides of (1) by {{{5}}}
and subtract from (2)
(2) {{{5n + 10d = 210}}}
(1) {{{-5n - 5d = -150}}}
{{{5d = 60}}}
{{{d = 12}}}
and, since
{{{n + d = 30}}}
{{{n + 12 = 30}}}
{{{n = 18}}}
There are 18 nickels and 12 dimes
check:
(2) {{{5n + 10d = 210}}}
{{{5*18 + 10*12 = 210}}}
{{{90 + 120 = 210}}}
{{{210 = 210}}}
OK