Question

Peter has $135 and saves $55 each week. Sue has $850 and gives $25 each week to her mother. For how many weeks will Sue have more money than Peter?

A. 2 weeks
B. 6 weeks
C. 4 weeks
D. 9 weeks

Answer 1

To determine how many weeks Sue will have more money than Peter, we can set up an inequality and solve for 'n'. After solving, we find that Sue will have more money than Peter after 9 weeks.

Step-by-step explanation:

To determine how many weeks Sue will have more money than Peter, we need to compare their respective savings over time.

Let's represent the number of weeks as 'n'. Peter saves $55 each week, so the amount of money he will have after 'n' weeks is 135 + 55n. Similarly, Sue gives $25 each week to her mother, so the amount of money she will have after 'n' weeks is 850 - 25n.

We need to find the value of 'n' for which Sue will have more money than Peter. Setting up the inequality 850 - 25n > 135 + 55n, we can solve for 'n'.

850 - 25n > 135 + 55n

850 - 135 > 25n + 55n

715 > 80n

715/80 > n

8.9375 > n

Since 'n' represents the number of weeks, it must be a whole number. Therefore, 'n' can be 9 or greater. This means that Sue will have more money than Peter after 9 weeks.

The correct answer is D. 9 weeks.