SOLUTION: A collection of quarters and dimes is worth $4.35. There are 24 coins in all. How many of each are there?

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Question 748298: A collection of quarters and dimes is worth $4.35. There are 24 coins in all. How many of each are there?
Answer by timvanswearingen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let q represent the number of quarters and d represent the number of dimes.
Since there are 24 coins:
q%2Bd=24
Let's solve this for one of the variables, I'll choose q. So subtract d from both sides:
q=24-d


Since quarters are worth .25 and dimes are worth .10, we have another equation:
.25q%2B.1d=4.35
Now, we can use the equation we found earlier (q=24-d) and plug in 24-d for q:
.25q%2B.1d=4.35
.25%2824-d%29%2B.1d=4.35
Now distribute and combine like terms:
6-.25d%2B.1d=4.35
6-.15d=4.35
Subtract 6 from both sides:
-.15d+=+-1.65
Divide both sides by -.15:
d=11
Thus, there are 11 dimes.
We found that q=24-d, so:
q=24-11
q=13
There are 13 quarters and 11 dimes.