Question

Kate and Nora each have a sum of money. The ratio of the amount of money Kate has to that of Nora is 3 : 5. After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9. Find the sum of money Kate had initially.

Answer 1

Given:

The ratio of the amount of money Kate has to that of Nora is 3 : 5.

After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.

To find:

The sum of money Kate had initially.

Solution:

Let the initial amount of money Kate and Nora have are 3x and 5x respectively.

After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.

The amount of Kate = 3x+150

The amount of Nora = 5x-150

Now,

`(3x+150)/(5x-150)=(7)/(9)`

`9(3x+150)=7(5x-150)`

`27x+1350=35x-1050`

`1350+1050=35x-27x`

`2400=8x`

Divide both sides by 8.

`300=x`

Putting x=300 in 3x, to get the amount of money Kate has initially.

`3(300)=900`

Therefore, the Kate initially had $900.