Question

The ratio of Alice's savings to Bernice's savings was 5 : 4 at first. After Alice had spent $20 and Bernice had received $10, both of them had the same amount of money. How much money did Bernice have at first?

Answer 1

Given:

a.) The ratio of Alice's savings to Bernice's savings was 5 : 4 at first.

b.) After Alice had spent $20 and Bernice had received $10, both of them had the same amount of money.

Let,

x = the savings the had in $.

Alice's savings = 5x

Bernice Savings = 4x

After Alice had spent $20 and Bernice had received $10, the equation will be:

`\text{ 5x - 20 = 4x + 10}`

Let's now find x.

5x - 20 = 4x + 10

5x - 4x = 10 + 20

x = 30 = $30

Let's now determine how much money did Bernice have at first.

Bernice's money = 4x = 30(4) = $120

Therefore, Bernice's had $120 at first.