SOLUTION: A collection of 102 nickels, dimes, and quarters is worth $13.60. There are 14 more nickels than dimes. How many quarters are there?

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Question 349022: A collection of 102 nickels, dimes, and quarters is worth $13.60. There are 14 more nickels than dimes. How many quarters are there?
Answer by mananth(16946) About Me  (Show Source):
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A collection of 102 nickels, dimes, and quarters is worth $13.60. There are 14 more nickels than dimes. How many quarters are there?
dimes = x
nickels = x+14
quarters = 102 -( x+x+14)
=102-(2x+14)
=102-2x-14
=88-2x
...
10x+5(x+14)+25(88-2x)=1360
10x+5x+70+2200-50x=1360
-35x=-2270+1360
-35x=-910
x= -910/-35
x= 26 dimes
nickels = 26+14 = 40
quarters = 88-52=36
...
CHECK
40 *5 +26*10+ 36*25=1360