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Multiple Choice
Suppose Refrigerator A costs \$1,200 with annual operating costs of \$200, and Refrigerator B costs \$900 with annual operating costs of \$300. After how many years will the average annual cost of the two refrigerators be equal?
A
3 years
B
9 years
C
6 years
D
4 years
Verified step by step guidance
1
Step 1: Define the average annual cost formula for each refrigerator. The average annual cost is calculated as the total cost (purchase price + cumulative operating costs) divided by the number of years.
Step 2: Write the equations for the average annual cost of Refrigerator A and Refrigerator B. For Refrigerator A: \( \text{Average Annual Cost}_A = \frac{1200 + 200n}{n} \), and for Refrigerator B: \( \text{Average Annual Cost}_B = \frac{900 + 300n}{n} \), where \( n \) is the number of years.
Step 3: Set the two average annual cost equations equal to each other to find the year \( n \) when the costs are equal: \( \frac{1200 + 200n}{n} = \frac{900 + 300n}{n} \).
Step 4: Simplify the equation by multiplying through by \( n \) (assuming \( n \neq 0 \)) to eliminate the denominator: \( 1200 + 200n = 900 + 300n \).
Step 5: Solve for \( n \) by isolating \( n \) on one side of the equation: \( 1200 - 900 = 300n - 200n \), which simplifies to \( n = \frac{300}{100} \).