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

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) (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:

Let's solve this for one of the variables, I'll choose q. So subtract d from both sides:

Since quarters are worth .25 and dimes are worth .10, we have another equation:

Now, we can use the equation we found earlier (q=24-d) and plug in 24-d for q:

Now distribute and combine like terms:

Subtract 6 from both sides:

Divide both sides by -.15:

Thus, there are 11 dimes.
We found that q=24-d, so:

There are 13 quarters and 11 dimes.

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