Question

sean gets international candies sent to his apartment every month from tastytrek, which has two payment plans. - no plan, with a cost of $16 per month - economy plan, with a membership fee of $64 and a cost of $8 per month question 5: what is the number of months where the cost of no plan and a economy plan are the same (known as the \breakeven point\)? question 6: if sean expects to get 5 months, which plan should he choose?

Explanation:

Step1: Define variables and cost equations

Let $m$ = number of months.
Cost of No Plan: $C_n = 16m$
Cost of Economy Plan: $C_e = 64 + 8m$

Step2: Set costs equal for breakeven

Set $C_n = C_e$:
$16m = 64 + 8m$

Step3: Solve for $m$

Subtract $8m$ from both sides:
$16m - 8m = 64$
$8m = 64$
Divide by 8:
$m = \frac{64}{8} = 8$

Step4: Calculate costs for 5 months

No Plan cost: $C_n = 16 \times 5 = 80$
Economy Plan cost: $C_e = 64 + 8 \times 5 = 64 + 40 = 104$

Step5: Compare costs for 5 months

Since $80 < 104$, the No Plan is cheaper.

Answer:

Question 5: 8
Question 6: No plan