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 $3,000< 75 \mathrm{c}$ 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
\boxed{\text{Henry should choose Plan A only if he expects to need more than 40 cleanings in 1 year}}
Step 1 ：Solve the inequality: \(3000 < 75c\)
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}}
