Question

Grace spent 1/8 of her money on a bag. 1/2 of her money on a jacket and the rest on a dress.

a/ what fraction of her money did she spent on the dress?
b/ if she spent $72 more on the dress than on the bag, how much money did she have at first?

Answer 1

Grace spent 3/8 of her money on the dress. A system of equations based on the money spent on the bag and the additional $72 spent on the dress compared to the bag allows us to calculate that Grace initially had $288.

Step-by-step explanation:

The student wants to know what fraction of Grace's money was spent on the dress and how much money Grace originally had, given she spent $72 more on the dress than on the bag.

Part A

Fraction spent on the dress: Grace spent 1/8 on the bag and 1/2 on the jacket. Adding these fractions gives us the total fraction spent on the bag and jacket combined:

1/8 + 1/2 = 1/8 + 4/8 = 5/8

Since Grace spent 5/8 of her money on the bag and jacket, she must have spent the remainder on the dress. The remainder is 1 - 5/8 = 3/8. Therefore, she spent 3/8 of her money on the dress.

Part B

Initial amount of money: Given that Grace spent $72 more on the dress than on the bag:

Let the total amount of money be x. Then, the amount spent on the bag is x/8. Since the dress costs $72 more than the bag, the amount spent on the dress is x/8 + $72.

But we know that the amount spent on the dress represents 3/8 of the total money, so we set up the equation:

3/8 * x = x/8 + $72

By solving for x, we find:

3x = x + $576

2x = $576

x = $288

Grace originally had $288.