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 use variables to represent the unknowns:

Let's say that x is the number of dimes Peter has

Let's say that y is the number of quarters Peter has

From the problem, we know that the total value of his coins is $19.20. We can write an equation based on this information:

0.1x + 0.25y = 19.2

We also know that the number of quarters is 19 more than three times the number of dimes. We can write another equation based on this information:

y = 3x + 19

Now we have two equations and two variables, so we can solve for x and y.

Substitute the second equation into the first equation:

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

Simplify and solve for x:

0.1x + 0.75x + 4.75 = 19.2

0.85x = 14.45

x = 17

Now that we know x, we can use the second equation to find y:

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

Therefore, Peter has 17 dimes and 70 quarters.