Question

You are adding up the quarters and dimes from your piggy bank so you can buy a new book. you have a total of 50 coins that add up to $9.80. how many quarters and how many dimes do you have?

Answer 1

Let $Q$ be the number of quarters you have, and $D$ be the number of dimes you have. With the information provided above, you have the following equation:

$Q + D = 50$

Next, you know the value of a quarter is 0.25, and the value of a dime is 0.10, so you can set up the next equation:

$0.25Q + 0.10D = 9.80$

Substituting the first equation into the second leads to the following:

$0.25(50 - D) + 0.10D = 9.80$

Solving for $D$ will give you the number of dimes you have, and then you can easily figure out how many quarters you have as well.