158k views
3 votes
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?

User M S Gadag
by
8.2k points

1 Answer

0 votes

Answer:

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.

User Gruangly
by
8.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories