SOLUTION: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80. a) set up a sy

Algebra ->  Sequences-and-series -> SOLUTION: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80. a) set up a sy      Log On


   

Question 1141885: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80.
a) set up a system if equations to represent the situation.
b) find the number of quarters in the bank.

Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the actual number of dimes
Let +q+ = the actual number of quarters
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(1) +10d+%2B+25q+=+690+ ( in cents )
(2) +25d+%2B+10q+=+780+ ( in cents )
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(2) +5d+%2B+2q+=+156+
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Multiply both sides of (2) by +2+
(1) +10d+%2B+25q+=+690+
(2) +-10d+-+4q+=+-312+
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+21q+=+378+
+q=+18+
Plug this result back into (1) or (2)
(2) +5d+%2B+2%2A18+=+156+
(2) +5d+=+156+-+36+
(2) +5d+=+120+
(2) +d+=+24+
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There are 18 quarters in the bank
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check:
(2) +25d+%2B+10q+=+780+
(2) +25%2A24+%2B+10%2A18+=+780+
(2) +600+%2B+180+=+780+
OK
You can check (1)

Answer by josgarithmetic(39617) About Me  (Show Source):