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,

$\dfrac{3x+150}{5x-150}=\dfrac{7}{9}$

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

$27x+1350=35x-1050$

$1350+1050=35x-27x$

$2400=8x$

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.