A cleaning service offers its customers a choice between two plans.
- Plan $A$ costs $$ 3, 000$ and includes 1 year of an unlimited number of cleanings.
- Plan B costs $$ 75$ per cleaning.
Henry wants to choose the less expensive plan. He uses the inequality $3, 000 < 75 c$ to decide which plan to choose based on the number of cleanings $(c)$ he expects to need. Based on the solution of the inequality, which statement about Henry's choice of plan is true?

A. Henry should choose Plan A only if he expects to need fewer than 40 cleanings in 1 year.
B. Henry should choose Plan $A$ only if he expects to need more than 40 cleanings in 1 year.
C. Henry can choose either plan and pay the same amount if he expects to need fewer than 40 cleanings in 1 year.
D. Henry can choose either plan and pay the same amount if he expects to need more than 40 cleanings in 1 year.

Answer

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Answer

\boxed{\text{Henry should choose Plan A only if he expects to need more than 40 cleanings in 1 year}}

Steps

Step 1 ：Solve the inequality: $3000 < 75 c$

Step 2 ：Divide both sides by 75: $\frac{3000}{75} < c$

Step 3 ：Simplify: $40 < c$

Step 4 ：\boxed{\text{Henry should choose Plan A only if he expects to need more than 40 cleanings in 1 year}}