Question

Ivan had saved $500 from his summer job. He will need $75 per month

when he returns to school in the fall, but wants to keep at least $50 in
reserve. Which of the following inequalities best describes the number of
months, m, Ivan can use his funds, assuming there are no other additions
to or withdrawals from his savings?
Choose 1 answer:
500-75m < 50
500+ 75m < 50
500-75m 50
500+ 75m2 50

Answer 1

The inequality that best represents the number of months Ivan can use his funds without going below his $50 reserve is 500 - 75m ≥ 50. Simplifying this, Ivan can afford his expenses for at most 6 months.

Step-by-step explanation:

The question relates to forming an inequality to represent a financial situation. In this case, Ivan has $500 from his summer job and wants to ensure he has $50 in reserve after spending $75 each month on expenses once he returns to school. To find the number of months, m, that he can use his funds without going below his $50 reserve, we can set up the following inequality:

500 - 75m ≥ 50

This inequality can be simplified by subtracting 50 from both sides, resulting in:

450 ≥ 75m

To find m, we divide both sides by 75:

6 ≥ m

This means that Ivan can use his funds for at most 6 months before his savings reach his $50 reserve limit.

Now, let's review the provided options to find the correct inequality that represents Ivan's situation:

• 500 - 75m < 50 (Incorrect because it should be an inequality including 50 as the reserve limit)
• 500 + 75m < 50 (Incorrect because his savings will decrease over time, not increase)
• 500 - 75m ≥ 50 (Correct, as it shows the savings should be at least $50 after spending each month)
• 500 + 75m ≥ 50 (Incorrect, same mistake as the second option)

Therefore, the correct inequality is 500 - 75m ≥ 50.