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.

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,

Divide both sides by 8.

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

Therefore, the Kate initially had $900.

hi there!

question 1 answer: p/q can be terminating when q = 5^m * 2^n

question 2 answer: -1 and -1

question 3 answer: -4

question 4 answer: 5/12

hope this : )