Question 658455: I used quarters to pay a loan from Brad. If I had paid using nickels, I would have needed 72 more of them. How much did I owe Brad?
We somehow figured out that the amount is $4.50 but have no idea how we figured it out! I think it was trial and error. The numbers $3.60 and 14.4 keep coming up...? Please help, my brain is exploding trying to help my son with this question.
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website! I used quarters to pay a loan from Brad. If I had paid using nickels, I would have needed 72 more of them. How much did I owe Brad?
We somehow figured out that the amount is $4.50 but have no idea how we figured it out! I think it was trial and error. The numbers $3.60 and 14.4 keep coming up...? Please help, my brain is exploding trying to help my son with this question.
Are you saying that if you used nickels, you would’ve needed 72 more than the amount of quarters used? If so, the solution follows.
Let amount of quarters used to pay loan be Q
Then amount of nickels that would be needed to pay the loan = Q + 72
The value of the quarters or the amount you paid Brad = .25Q, or value of the nickels needed to pay Brad = .05(Q + 72)
Since these 2 amounts have the same value, we can say that:
.25Q = .05(Q + 72)
.25Q = .05Q + 3.6
.25Q - .05Q = 3.6
.2Q = 3.6
Q, or amount of quarters used to pay loan =  , or 18
This means that the amount of the loan, using quarters, was: .25(18), or $
Also, using nickels, we have: .05(18 + 72), or .05(90), or $
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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