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:

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<reasoning>

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.
</reasoning>

<answer>
<mcq-correct>Plan A</mcq-correct>
<mcq-option>Plan B</mcq-option>
<mcq-option>Plan C</mcq-option>
<mcq-option>Plan D</mcq-option>
</answer>

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Answer:

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<reasoning>

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.
</reasoning>

<answer>
<mcq-correct>Plan A</mcq-correct>
<mcq-option>Plan B</mcq-option>
<mcq-option>Plan C</mcq-option>
<mcq-option>Plan D</mcq-option>
</answer>

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