Question

Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value $19.20. The number of quarters was nineteen more than three times the number of dimes. How many quarters and how many dimes did Peter have?

Answer 1

Explanation:

Let's start by defining our variables.

Let x be the number of dimes that Peter has.

Then the number of quarters that Peter has is 3x + 19 (since he has 19 more quarters than three times the number of dimes).

Next, we can set up an equation to represent the total value of Peter's coins:

0.1x + 0.25(3x + 19) = 19.2

Simplifying and solving for x:

0.1x + 0.75x + 4.75 = 19.2

0.85x = 14.45

x = 17

So Peter has 17 dimes. To find the number of quarters, we can substitute x = 17 into our expression for the number of quarters:

3x + 19 = 3(17) + 19 = 70

Therefore, Peter has 70 quarters.

To check our work, we can verify that the total value of Peter's coins is indeed $19.20:

0.1(17) + 0.25(70) = 1.7 + 17.5 = 19.2

So our solution is correct. Peter has 17 dimes and 70 quarters.