SOLUTION: Andria has $16 worth of quarters and dimes. If Andria has 2 1/2 times as many dimes as she does quarters, how many quarters does she have?

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Question 1158389: Andria has $16 worth of quarters and dimes. If Andria has 2 1/2 times as many dimes as she does quarters, how many quarters does she have?
Found 2 solutions by Shin123, MathTherapy:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let q and d be the amount of quarters and dimes she has, respectively. We have system%2825q%2B10d=1600%2Cd=%285%2F2%29q%29 Rearranging, we have system%2810d%2B25q=1600%2Cd-%285%2F2%29q=0%29.
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++10%5Cd+%2B+25%5Cq+=+1600%2C%0D%0A++++1%5Cd+%2B+-2.5%5Cq+=+0+%29%0D%0A++We'll use substitution. After moving 25*q to the right, we get:
10%2Ad+=+1600+-+25%2Aq, or d+=+1600%2F10+-+25%2Aq%2F10. Substitute that
into another equation:
1%2A%281600%2F10+-+25%2Aq%2F10%29+%2B+-2.5%5Cq+=+0 and simplify: So, we know that q=32. Since d+=+1600%2F10+-+25%2Aq%2F10, d=80.

Answer: system%28+d=80%2C+q=32+%29.

She has 32 quarters.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Andria has $16 worth of quarters and dimes. If Andria has 2 1/2 times as many dimes as she does quarters, how many quarters does she have?
Are you confused yet by what the other person did? If so, read on!

Let the number of quarters be Q

Then number of dimes = 2.5Q

We then get: .1D + .25Q = 16

.1(2.5Q) + .25Q = 16 ----- Substituting 2.5Q for D

Continue to solve for Q, the number of quarters, and you should get highlight_green%28matrix%281%2C3%2C+32%2C+of%2C+them%29%29