What is the inequality for this word problem?

A local movie theater is struggling to maintain customers. At their peak last year, they earned $20,000 per day in sales. Since then, they are losing approximately $400 each week. In order to stay in business, they need to earn at least $8,000 in sales. How many weeks until the movie theater is losing money?

A. $400w + 20000 \geq 8000$
B. $400w + 20000 \leq 8000$
C. $400w - 20000 \geq 8000$
D. $400w - 20000 \leq 8000$

The correct inequality for the word problem is '20000 - 400w >= 8000'. This describes how long the movie theater can maintain its business before it starts losing money, based on its weekly loss.

Explanation:

The correct inequality for this word problem is

d. 20000 - 400w >= 8000

. This inequality represents the scenario described within the word problem: the movie theater initially made $20,000 per day, but is losing $400 every week. In order to not lose money, they need to maintain a minimum income of $8,000. To solve for '

w

', which is the number of weeks before they start losing money, we need to rearrange the equation to isolate '

w

', that is when $20,000$ - $400$w becomes less than $8000$. As long as this inequality holds, the theater won't lose money. As such, our inequality describes the number of weeks ('

w

') before this movie theater starts experiencing financial losses.

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