Question

Jill has $1.25 in her pocket. The money is in quarters and dimes. There are a total of 8 coins. How many quarters and dimes does Jill have in her pocket?

Answer 1

• 3 quarters
• 5 dimes

Explanation:

Let q represent the number of quarters (the higher-value coin). Then 8-q is the number of dimes, and Jill's total amount in change is ...

0.25q +0.10(8-q) = 1.25

0.15q + 0.80 = 1.25 . . . . . . . eliminate parentheses

0.15q = 0.45 . . . . . . . . . . . . . subtract 0.80

q = 3 . . . . . . . . . . . . . . . . . . . . divide by 0.15

the number of dimes is 8-q = 8-3 = 5.

Jill has 3 quarters and 5 dimes.

Answer 2

Answer:Jill has 5 dimes and 3 quarters.

Explanation:

The worth of a dime is 10 cents. Converting to dollars, it becomes

10/100 = $0.1

The worth of a quarter is 25 cents. Converting to dollars, it becomes

25/100 = $0.25

Let x represent the number of dimes that she has in her pocket.

Let y represent the number of quarter that she has in her pocket.

There are a total of 8 coins. This means that

x + y = 8

Jill has $1.25 in her pocket. This means that

0.1x + 0.25y = 1.25 - - - - - - - - - - - 1

Substituting x = 8 - y into equation 1, it becomes

0.1(8 - y) + 0.25y = 1.25

0.8 - 0.1y + 0.25y = 1.25

- 0.1y + 0.25y = 1.25 - 0.8

0.15y = 0.45

y = 0.45/0.15 = 3

x = 8 - y = 8 - 3

x = 5