Question

Dave and Adrea are saving to buy new cell phones. Dave has $40 and plans to save $10 per week. Adrea has $100 and plans to save $6 per week. In how many weeks will Dave have more money saved than Adrea? If w represents the number of weeks, write an inequality that could be used to solve this word problem.

Answer 1

To determine when Dave will have more saved than Adrea, the inequality 40 + 10w > 100 + 6w suggests that after more than 15 weeks, Dave's savings will exceed Adrea's.

Step-by-step explanation:

To find out after how many weeks Dave will have more money saved than Adrea, we need to compare their savings as a function of time. Dave starts with $40 and saves $10 per week, so his savings after w weeks can be expressed as 40 + 10w. Adrea starts with $100 and saves $6 per week, making her savings 100 + 6w. We need to find the value of w for which Dave's savings exceed Adrea's savings.

To determine the number of weeks when Dave will have more money saved than Adrea, we can set up an inequality:

40 + 10w > 100 + 6w

Subtracting 6w from both sides, we get:

4w > 60

Dividing both sides by 4, we find:

w > 15

So, after more than 15 weeks, Dave will have more money saved than Adrea.