Question 266429
{{{n}}} = number of nickels
{{{d}}} = number of dimes
{{{q}}} = number of quarters
given:
(1) {{{5n + 10d + 25q = 950}}} (in cents)
(2) {{{n = (2/3)*d}}}
(3) {{{d = (1/2)*q}}}
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From (3)
{{{q = 2d}}}
By substitution:
(1) {{{5*(2/3)*d + 10d + 25*(2d) = 950}}}
{{{(10/3)*d + 10d + 50d = 950}}}
{{{10d + 30d + 150d = 2850}}}
{{{190d = 2850}}}
{{{d = 15}}}
From (3)
{{{q = 2d}}}
{{{q = 30}}}
There are 30 quarters
check answer:
(2) {{{n = (2/3)*d}}}
{{{n = (2/3)*15}}}
{{{n = 10}}}
and
(1) {{{5n + 10d + 25q = 950}}}
(1) {{{5*10 + 10*15 + 25*30 = 950}}}
{{{50 + 150 + 750 = 950}}}
{{{950 = 950}}}
OK