SOLUTION: Christine has $5 in quarters,nickles and dimes. She has 3x as much money in nickles as she does in dimes, and she has 5x as much money in quarters as she does in nickles. How much

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Christine has $5 in quarters,nickles and dimes. She has 3x as much money in nickles as she does in dimes, and she has 5x as much money in quarters as she does in nickles. How much       Log On

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Question 549688: Christine has $5 in quarters,nickles and dimes. She has 3x as much money in nickles as she does in dimes, and she has 5x as much money in quarters as she does in nickles. How much does she have of each?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of nickels
Let d = number of dimes
Let q = number of quarters
given:
(1) +5n+=+3%2A%2810d%29+
(2) +25q+=+5%2A%285n%29+
(3) +5n+%2B+10d+%2B+25q+=+500+ ( in cents )
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This is 3 equations and 3 unknowns
(1) +5n+=+30d+
(1) +d+=+%281%2F6%29%2An+
and
(2) +q+=+n+
Substitute (1) and (2) into (3)
(3) +5n+%2B+10%2A%281%2F6%29%2An+%2B+25n+=+500+
(3) +%28+5+%2B+5%2F3+%2B+25+%29%2An+=+500+
(3) +%28+15%2F3+%2B+5%2F3+%2B+75%2F3+%29%2An+=+500+
(3) +%28+95%2F3+%29%2An+=+500+
(3) +n+=+%283%2F95%29%2A500+
You can finish