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.

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.