Question

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

Answer 1

$130

Explanation:

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

(x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

4(x/2 -58) = (x/2 -37)

2x -232 = x/2 -37 . . . . . . eliminate parentheses

3/2x = 195 . . . . . . . . . . . . add 232-x/2

x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

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Alternate solution

The difference in their spending is $58 -37 = $21. This is the same as the difference in their final balances. That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7. Their ending total is 1+4 = 5 ratio units, or $35. The total they started with is $58 +37 +35 = $130.