SOLUTION: You have 8 coins consisting of nickels, dimes, and quarters and totaling 1.10. If the nickels and dimes along total 35 cents, how many quarters do you have? How many dimes? and ni

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: You have 8 coins consisting of nickels, dimes, and quarters and totaling 1.10. If the nickels and dimes along total 35 cents, how many quarters do you have? How many dimes? and ni      Log On

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Question 763736: You have 8 coins consisting of nickels, dimes, and quarters and totaling 1.10. If the nickels and dimes along total 35 cents, how many quarters do you have? How many dimes? and nickels?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of dimes you have
Let +d+ = number of dimes you have
Let +q+ = number of quarters you have
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given:
(1) +n%2B+d+%2B+q+=+8+
(2) +5n+%2B+10d+%2B+25q+=+110+ ( in cents )
(3) +5n+%2B+10d+=+35+
--------------------
Substitute (3) into (2)
(2) +35+%2B+25q+=+110+
(2) +25q+=+75+
(2) +q+=+3+
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(1) +n%2B+d+%2B+3+=+8+
(1) +n+%2B+d+=+5+
and,
(3) +5n+%2B+10d+=+35+
(3) +n+%2B+2d+=+7+
Subtract (1) from (3)
(3) +n+%2B+2d+=+7+
(1) +-n+-d+=+-5+
+d+=+2+
and, since
(1) +n+%2B+d+=+5+
(1) +n+=+5+-+2+
(1) +n+=+3+
There are 3 nickels, 2 dimes, and 3 quarters
check:
(2) +5n+%2B+10d+%2B+25q+=+110+
(2) +5%2A3+%2B+10%2A2+%2B+25%2A3+=+110+
(2) +15+%2B+20+%2B+75+=+110+
(2) +110+=+110+
OK