Question

needs to have c cleanings, what is the least expensive plan?
least expensive plan for c:
raquel wants to get into shape at exercisebar, which has two payment plans:

• no plan, with a cost of $21 per session
• economy plan, with a subscription fee of $156 and a cost of $9 per session

question 5: what is the number of sessions where the cost of no plan and a economy plan are the same (known as the \breakeven point\)?
question 6: if raquel expects to have 7 sessions, which plan should she choose?

Explanation:

Step1: Define cost equations

Let $x$ = number of sessions.

• No plan cost: $C_{no} = 21x$
• Economy plan cost: $C_{eco} = 156 + 9x$

Step2: Find breakeven (Question5)

Set costs equal, solve for $x$:
$$21x = 156 + 9x$$
$$21x - 9x = 156$$
$$12x = 156$$
$$x = \frac{156}{12} = 13$$

Step3: Calculate costs for 7 sessions (Question6)

• No plan: $C_{no} = 21 \times 7 = 147$
• Economy plan: $C_{eco} = 156 + 9 \times 7 = 156 + 63 = 219$

Compare: $147 < 219$, so choose No plan.

Answer:

Question 5: 13
Question 6: No plan