SOLUTION: A collection of coins consists of nickels, dimes, and quarters. there are 4 less nickels than dimes. There are 26 coins in total. The total value of the collection is $3.10. Fine t

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Question 318136: A collection of coins consists of nickels, dimes, and quarters. there are 4 less nickels than dimes. There are 26 coins in total. The total value of the collection is $3.10. Fine the number of each type of coin.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let N be the number of nickels, D dimes, Q quarters.
.
.
"There are 26 coins in total."
1.N%2BD%2BQ=26
.
.
.
"there are 4 less nickels than dimes"
2.N=D-4
.
.
.
"The total value of the collection is $3.10"
3.5N%2B10D%2B25Q=310
Substitute eq. 2 into eq. 1 and eq. 3,
D-4%2BD%2BQ=26
4.2D%2BQ=30
.
.
5%28D-4%29%2B10D%2B25Q=310
5D-20%2B10D%2B25Q=310
5.15D%2B25Q=330
Multiply eq. 4 by (-25) and add to eq. 5.
-50D-25Q%2B15D%2B25Q=-750%2B330
-35D=-420
highlight%28+D=12%29
Then,
N=D-4
highlight%28+N=8%29
and finally,
8%2B12%2BQ=26
highlight%28+Q=6%29