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Question

Damien has some quarters and dimes. He has  coins worth a total of  . How many of each type of coin does he have?

Answer 1

Let Q=the number of quarters, D=the number of dimes. Since quarters are 25 cents each and dimes are 10 cents each, we can determine the total value by multiplying .25Q+.1D, which is the number of quarters times the value of the quarters plus the number of dimes times the value of the dimes. We set this equal to our total to get equation 1, which says:.25Q+.1D=2.35. We can set up equation 2 by saying Q+D=13. We then use substitution or elimination or whichever method you prefer to determine the answer. I will use substitution here. Q=13-D. Then, by equation 1, .25(13-D)+.1D=2.35. This yields by the distributive property 3.25-.25D+.1D=2.35. By combining like terms, we get -.15D=-0.9. By division, D=6. We plug this back into equation 2 to get 7 quarters.

I hope this helped.