Question

12 + 20x < 4 + 22

Which word problem could the inequality represent?
A. At gym A there is a startup fee of $12, and each month costs $20. At gym B, the startup fee is 4, but each month costs $22. After which numbers of months would gym B be more expensive?
B. Sasha deposits $4 and adds $22 every week. George deposits $12 and adds $10 every 2 weeks. After which numbers of weeks will Sasha have saved more than George?
C. Plan A charges 12¢ for the first minute of an international call and 20¢ for each additional minute, while Plan B charges 4¢ for the first minute and 22¢ for each additional minute. Which plan, in minutes, makes Plan B more expensive?
D. Wu and Liam start driving from the same point. After mile marker 4, Wu stops to rest every 22 miles, while after mile marker 12, Liam stops to rest every 20 miles. If they arrive at the same destination, will Wu have made more stops?

Answer 1

The inequality 12 + 20x < 4 + 22 represents a scenario where two different gym memberships are being compared, and it identifies when one gym becomes more expensive than the other. After simplification, the inequality x < 0.7 corresponds to the number of months after which gym B would be more expensive than gym A.

Step-by-step explanation:

The inequality 12 + 20x < 4 + 22 can represent a comparison of costs for gym memberships, weekly savings, international call plans, or stops during a trip. When we simplify the inequality, we get 20x < 14, or x < 0.7 after dividing both sides by 20. This tells us that for less than 0.7 units of x, one option will be cheaper than the other. The correct word problem that corresponds to this inequality is the one about gym memberships, as it deals with initial startup fees and ongoing monthly costs (Option A).

In this context, x represents the number of months, the 12 represents the startup fee for gym A, 20x is the monthly cost at gym A, 4 is the startup fee for gym B, and 22 is the monthly cost for gym B. The inequality suggests that for fewer than 0.7 months (which is not a practical unit for months, implying that immediately from the start), gym B would be more expensive than gym A.