Question

1. (5 points) felicias current refrigerator costs approximately $20 a month in electricity to run. a new energy efficient refrigerator costs $1200 to purchase, but only costs $6.50 a month in electricity to run. after approximately how many months does the energy efficient refrigerator pay for itself? fully explain how you arrived at your answer.

Explanation:

Step1: Set up cost equations

Let \(x\) be the number of months.
The cost of the current refrigerator is \(C_{1}=20x\).
The cost of the new energy - efficient refrigerator is \(C_{2}=1200 + 6.5x\).

Step2: Find when costs are equal

Set \(C_{1}=C_{2}\), so \(20x=1200 + 6.5x\).
Subtract \(6.5x\) from both sides: \(20x-6.5x=1200\).
\(13.5x = 1200\).
Solve for \(x\): \(x=\frac{1200}{13.5}\approx88.89\).

Answer:

Approximately \(89\) months.