Question 764109: A vending machine's coin box contains nickels, dimes, and quarters. The total number of coins in the box is 336. The number of dimes is three time the number of nickels and quarters together. If the box contains 33 dollars and 20 cents, find the number of nickels, dimes, and quarters that it contains.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A vending machine's coin box contains nickels, dimes, and quarters. The total number of coins in the box is 336. The number of dimes is three time the number of nickels and quarters together. If the box contains 33 dollars and 20 cents, find the number of nickels, dimes, and quarters that it contains.
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let n=number of nickels
let q=number of quarters
let d=number of dimes
..
d=3(n+q)=3n+3q
d+n+q=336
.10d+.05n+.25q=33.20
..
3n+3q+n+q=336
.10(3n+3q)+.05n+.25q=33.20
..
4n+4q=336
.3n+.3q+.05n+.25q=33.20
..
4n+4q=336
.35n+.55q=33.20
..
1.4n+1.4q=117.6
1.4n+2.2q=132.8
subtract:
0.8q=15.2
q=19
4n=336-4q=336-76=260
n=65
d=3n+3q=252
check:
19 quarters=19*.25=4.75
65 nickels=.05*65=3.25
252 dimes=252*.1=25.20
4.75+3.25+25.20=33.20
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