SOLUTION: question #16 the total value of the dimes and quarters in a coin bank is $3.70. if the dimes were quarters and the quarters were dimes, the total value of the coins would be $2.

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Question 217473: question #16
the total value of the dimes and quarters in a coin bank is $3.70. if the dimes were quarters and the quarters were dimes, the total value of the coins would be $2.95. find the number of quarters in the coin bank




Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
question #16
The total value of the dimes and quarters in a coin bank is $3.70. If the dimes were quarters and the quarters were dimes, the total value of the coins would be $2.95. find the number of quarters in the coin bank.

Step 1. Let x be the number of dimes.

Step 2. Let y be the number of quarters.

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%2B0.25y=3.70 since the total value of the dimes and quarters in a coin bank is $3.70.

Step 6. Then 0.10y%2B0.25x=2.95 since the dimes were quarters and the quarters were dimes, the total value of the coins would be $2.95

Step 7. Based on Steps 5 and 6 we have the following linear system of equations which will be solved by elimination.

0.10x%2B0.25y=3.70
0.25x%2B0.10y=2.95

Step 8. Let's get rid of the decimal point by multiplying both equations by 100.

10x%2B25y=370 Equation A
25x%2B10y=295 Equation B

Step 9. Multiply Equation A by by 2%2F5 to both equations to simplify the problem a bit.

%2810x%29%2A%282%2F5%29%2B25%2A%282%2F5%29=370%2A%282%2F5%29

4x%2B10y=148 Equation A1
25x%2B10y=295 Equation B

Step 10. Subtract Equation A1 from Equation B to get the following:

%2825-4%29x%2B%2810-10%29y=295-148

21x=147

Step 11. Divide 11 to both sides of the equation

21x%2F21=147%2F21

x=7

Step 12.Substitute x=7 into 4x%2B10y=148 to find y

4%2A7%2B10y=148

28%2B10y=148

Step 13. Subtract 28 from both sides of the equation

28%2B21y-28=148-28

10y=120

Step 14. Divide by 10 to both sides of the equation.

10y%2F10=120%2F10

y=12

Step 15. Now check if x=7 and y=12 satisfies Equation B or 25x%2B10y=295

25%2A7%2B10%2A12=175%2B120=295 which is a true statement.

Step 16. ANSWER: In the coin bank there are 7 dimes and 12 quarters.

I hope the above steps and explanation were helpful.

For free Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry, please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your future studies.

Respectfully,
Dr J