SOLUTION: The total value of the quarters and dimes in a coin bank is $8.00. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35. Find the n
Question 230228: The total value of the quarters and dimes in a coin bank is $8.00. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35. Find the number of quarters in the bank.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website! The total value of the quarters and dimes in a coin bank is $8.00. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35. Find the number of quarters in the bank.
Step 1. Let x be the number of dimes
Step 2. Let y be the number of quarters since there are 16 coins in all.
Step 3. Let 0.10x be the dollar value of dimes.
Step 4. Let 0.25y be the dollar value of quarters.
Step 5. Then, 0.10x+0.25y=8.00 since the total value of the quarters and dimes in a coin bank is $8.00
Step 6. Then, 0.25x+0.10y=6.35 since if the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35
Step 7. From Steps 5 and 6, we have the following linear system of equations
Solve: We'll use substitution. After moving 0.25*y to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that y=26. Since , x=15.
Answer: .
Step 8. ANSWER: The number of dimes is 15 and the number of quarters is 26.
I hope the above steps and explanation were helpful.
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And good luck in your studies!
Respectfully,
Dr J
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