High School

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The ratio of the incomes of Lucy and Morgan is 5:8. The ratio of the savings of Lucy and Morgan is 3:5. Find the ratio of the expenditures of Lucy and Morgan, if Lucy saves 30% of her income.

A. 2/3
B. 7/11
C. 9/14
D. 15/23

Answer :

Final answer:

The ratio of the expenditures of Lucy and Morgan is found by first determining their savings from their incomes and then calculating their expenditures by subtracting savings from incomes. This results in a ratio of 7:11 for their expenditures. Therefore, the correct option is B.

Explanation:

Let us assume that Lucy's income is 5x and Morgan's income is 8x, where x represents a common factor in their incomes. Since Lucy saves 30% of her income, her savings are 0.3 × 5x = 1.5x. By the given savings ratio of Lucy to Morgan, which is 3:5, Morgan's savings can be represented as 5/3 × 1.5x = 2.5x.

Now, we can find their expenditures by subtracting savings from income. Lucy's expenditure is 5x - 1.5x = 3.5x. Morgan's expenditure is 8x - 2.5x = 5.5x.

So, the ratio of their expenditures will be Lucy's expenditure : Morgan's expenditure = 3.5x : 5.5x. Removing the common factor x, the simplified ratio of their expenditures is 7:11.

This means the correct answer to the question of what the ratio of the expenditures of Lucy and Morgan is, is 7:11 (option b).

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