Question 38305
A vending machine has $41.25 in it. There are 225 coins total and the machine only accepts nickels, dimes , and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
Variables:
d=number of dimes
n=number of nickels
q=number of quarters
Equations:
{{{.1d+.05n+.25q=41.25}}}
{{{d+n+q=225}}}
{{{d=2n}}}
Combine:
{{{-.1d-.1n-.1q=-22.5}}}
+
{{{.1d+.05n+.25q=41.25}}}
=
{{{-.05n+.15q=18.75}}}
and
{{{-d-n-q=-225}}}
+
{{{d-2n=0}}}
=
{{{-3n-q=-225}}}
Combine:
{{{3n-9q=-1125}}}
+
{{{-3n-q=-225}}}
=
{{{-10q=-1350}}}
{{{q=135}}}
Combine:
{{{-3n-q=-225}}}
{{{-3n-135=-225}}}
{{{-3n=-90}}}
{{{n=30}}}
combine:
{{{d+30+135=225}}}
{{{d+165=225}}}
{{{d=60}}}
So there are 60 dimes, 30 nickels, and 135 quarters.