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)   (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 be the number of dimes.

Step 2. Let be the number of quarters.

Step 3. Let be the dollar value of dimes.

Step 4. Let be the dollar value of quarters.

Step 5. Then, since the total value of the dimes and quarters in a coin bank is $3.70.

Step 6. Then 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.




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

Equation A
Equation B

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



Equation A1
Equation B

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





Step 11. Divide to both sides of the equation





Step 12.Substitute into to find y





Step 13. Subtract from both sides of the equation





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





Step 15. Now check if and satisfies Equation B or

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






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