Question 318136
Let N be the number of nickels, D dimes, Q quarters.
.
.
"There are 26 coins in total."
1.{{{N+D+Q=26}}}
.
.
.
"there are 4 less nickels than dimes"
2.{{{N=D-4}}}
.
.
.
"The total value of the collection is $3.10"
3.{{{5N+10D+25Q=310}}}
Substitute eq. 2 into eq. 1 and eq. 3,
{{{D-4+D+Q=26}}}
4.{{{2D+Q=30}}}
.
.
{{{5(D-4)+10D+25Q=310}}}
{{{5D-20+10D+25Q=310}}}
5.{{{15D+25Q=330}}}
Multiply eq. 4 by (-25) and add to eq. 5.
{{{-50D-25Q+15D+25Q=-750+330}}}
{{{-35D=-420}}}
{{{highlight( D=12)}}}
Then,
{{{N=D-4}}}
{{{highlight( N=8)}}}
and finally,
{{{8+12+Q=26}}}
{{{highlight( Q=6)}}}