Question

gina is comparing four long distance phone plans. the table shows the cost of each plan.

cost of phone plans
plan | monthly fee | cost per minute
a | $15 | $0.05
b | $5 | $0.15
c | $10 | $0.10
d | $20 | $0.20

if gina plans to use 500 minutes each month, the most cost effective plan is plan a, plan b, plan c, plan d.

Explanation:

Formulate the cost equations

Using the Linear Functions knowledge point, we define the total monthly cost \(C\) for \(x\) minutes of use as:

$$C = \text{Monthly Fee} + (\text{Cost per Minute} \times x)$$

Calculate the cost for Plan A

Using the Linear Functions knowledge point:

$$C_A = 15 + 0.05 \times 500 = 15 + 25 = 40$$

Calculate the cost for Plan B

Using the Linear Functions knowledge point:

$$C_B = 5 + 0.15 \times 500 = 5 + 75 = 80$$

Calculate the cost for Plan C

Using the Linear Functions knowledge point:

$$C_C = 10 + 0.10 \times 500 = 10 + 50 = 60$$

Calculate the cost for Plan D

Using the Linear Functions knowledge point:

$$C_D = 20 + 0.20 \times 500 = 20 + 100 = 120$$

Comparing the costs, Plan A is the cheapest at \$40.

Answer:

• Plan A (Correct answer)
• Plan B
• Plan C
• Plan D