SOLUTION: letty has $5 in nickels, dimes and quarters. She has 3 times as many nickels as dimes. She has 5 times as much money in quarters as she does in nickels. How many of each does sh

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Question 895738: letty has $5 in nickels, dimes and quarters. She has 3 times as many nickels as dimes. She has 5 times as much money in quarters as she does in nickels. How many of each does she have?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The count of each coin assigned variables n,d, q.

0.05n%2B0.1d%2B0.25q=5, accounts for dollar money quantity and should be simplified;
n%2B2d%2B5q=100.

n%2Fd=3 according to description, so n=3d.

0.25q%2F%280.05n%29=5 according to description, so 5q%2Fn=5, q%2Fn=1 meaning q=n.

System to solve is this:
highlight_green%28system%28n%2B2d%2B5q=100%2Cn=3d%2Cq=n%29%29

More than one solution path you can take.

Substitute for n:
q%2B2d%2B5q=100
2d%2B6q=100
d%2B3q=50
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q=3d, when substitute for n in the second equation of the listed system.

System now after eliminating n is:
highlight%28system%28d%2B3q=50%2Cq=3d%29%29

Continuing,
d%2B3%283d%29=50
d%2B9d=50
10d=50
highlight%28d=5%29

You can work through the other equations to solve for n and q.


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n=15, and therefore q=15.