Question

pierre gets international candies sent to his apartment every month from candypassport, which has two payment plans:

• no plan, with a cost of $13 per month
• simple plan, with an enrollment fee of $80 and a cost of $5 per month

question 5: what is the number of months where the cost of no plan and a simple plan are the same (known as the \breakeven point\)?

question 6: if pierre expects to get 13 months, which plan should he choose?

Explanation:

Step1: Define cost equations

Let $m$ = number of months.
No plan cost: $C_n = 13m$
Simple plan cost: $C_s = 80 + 5m$

Step2: Set costs equal for breakeven

Set $C_n = C_s$:
$$13m = 80 + 5m$$

Step3: Solve for $m$

Subtract $5m$ from both sides:
$$13m - 5m = 80$$
$$8m = 80$$
Divide by 8:
$$m = \frac{80}{8} = 10$$

Step4: Calculate cost for 13 months

No plan cost:
$$C_n = 13 \times 13 = 169$$
Simple plan cost:
$$C_s = 80 + 5 \times 13 = 80 + 65 = 145$$

Step5: Compare costs for 13 months

Since $145 < 169$, the Simple plan is cheaper.

Answer:

Question 5: 10
Question 6: Simple plan