Addie had $3.25 in fine and quarters. Her number of dimes is 8 more than her number of quarters, how many of each coin does she have?

Question

PLEASE ANSWER! (Addie had $3.25 in fine and quarters. Her number of dimes is 8 more than her number of quarters, how many of each coin does she have?)

Answer 1

Hi Adam K.

7 quarters

15 dimes

Total amount 3.25 in dimes and quarters; where the number of dimes is 8 more than the number of quarter

Let x = dimes

Let y = quarters

x + y = number of coins

Also we are given

Dimes, x = y + 8

As cost we have

0.10x + 0.25y = 3.25

Substituting we have

0.10(y + 8) + 0.25y = 3.25

0.10y + 0.8 + 0.25y = 3.25

Combine like terms

0.35y + 0.8 = 3.25

Subtract 0.8 from both sides of the equation

0.35y = 3.25 - 0.8

0.35y = 2.45

Divide both sides by 0.35

y = 2.45/0.35

y = 7

We have 7 quarters

x + 8 = 7 + 8 = 15 = Dimes

We have 15 Dimes

You can check the amounts in the equation

0.10x + 0.25y = 3.25

0.10(15) + 0.25(7)

1.50 + 1.75 = 3.25

I hope you find this useful.

Answer 2

Hello, Adam,

I assume by "fines," you meant dimes. Let D = dimes and Q = quarters. We know by summing the number of each times it's value we'll have $3.25. (first equation). The second tells us the number of dines is 8 more than the number of quaters. Substitute this into the first equation to get the third. Then solve for quarters, which is 7. That means we have 15 dimes. 7(0.25) + 15(0.1) = $3.25

Bob