Question

Justin has $3.25 worth of dimes and quarters. He has a total of 16 dimes and quarters all together. Determine the number of dimes and the number of quarters that Justin has.

Answer 1

By setting up a system of equations and solving for the variables representing the number of dimes and quarters, we determined that Justin has 5 dimes and 11 quarters.

Step-by-step explanation:

To determine the number of dimes and quarters that Justin has, we can set up a system of equations.

Let d represent the number of dimes and q represent the number of quarters. We know that Justin has a total of $3.25 and 16 coins in total.

We can create two equations:

1. 10d + 25q = 325 (Since dimes are worth 10 cents and quarters are worth 25 cents, and Justin has $3.25 total)
2. d + q = 16 (Since Justin has a total of 16 dimes and quarters)

Now, we can solve this system of equations. We can use the second equation to express d in terms of q: d = 16 - q.

Substituting d in the first equation gives us:

10(16 - q) + 25q = 325

160 - 10q + 25q = 325

15q = 165

q = 11

Now that we know there are 11 quarters, we can find the number of dimes by substituting q back into the equation d = 16 - q:

d = 16 - 11 = 5

Justin has 5 dimes and 11 quarters.