```Question 190515
Let d=no of dimes in the pay phone
. 2*d=no of quarters ("the number of quarters is twice the number of dimes")
.   n=no of nickels
.
We know that all coins total 500, so:
{{{d+2d+n=500}}} or..
{{{3d+n=500}}}
.
We also know that the value of the all the coins is \$88, so:
{{{(0.10)*d+(0.25)*2d+(0.05)*n=88}}}
.
Simplifying, we get:
{{{0.10d+0.5d+0.05n=88}}}
{{{0.6d+0.05n=88}}}
.
Let's try to express n as a function of d:
Subtract 0.6d from both sides:
.
{{{0.6d-0.6d+0.05n=88-0.6d}}}
{{{0.05n=88-0.6d}}}
.
Divide both sides by 0.05:
.
{{{0.05n/0.05=(88-0.6d)/0.05}}}
{{{n=88/0.05-0.6d/0.05}}}
{{{n=1760-12d}}}
.
We now have n expressed as a function of d.
Substitute this value of n, in the first equation:
.
{{{3d+n=500}}}
{{{3d+(1760-12d)=500}}}
{{{-9d+1760=500}}}
.
Subtract 1760 from both sides:
.
{{{-9d+1760-1760=500-1760}}}
{{{-9d=-1260}}}
.
Divide both sides by -9:
.
{{{-9d/(-9)=-1260/(-9)}}}
{{{d=140}}}
.
We have 140 dimes, 140*2=280 quarters, 500-140-280=80 nickels.
.
To check:
140*(0.1)+280*(0.25)+80*(0.05)=?88
14+70+4=?88
88=88```