Question

Your friend Bamey Fife was remodeling his kitchen. He went shopping for a new refrigerator. The salesman at AppliancesRUs showed Barmey two models. Model A was an LG Electronics 25 cubic feet fridge that would cost $1399.99 initially and the monthly electric cost would be about $92 per month. Model B, a Maytag 25 cubic feet refrigerator, was on sale for $1839.99 with a monthly electricity cost of about $43 per month. The salesman urged Bamey to buy model B, the Maytag refrigerator, because he claimed that the total cost would be less than the LG over the long term. Baney wonders, "Is the salesman giving good advice or is he just interested in getting more commission on a higher priced sale?" Some of the mathematics that we've learned so far can help you advise Barney. #1.) Write a linear function for each type of refrigerator for the cost, C, of buying it and operating it over several months. Let the independent variable be t to stand for time in months.

Answer 1

C₁ = 1399.99 + 92t₁

C₂ = 1839.99 + 43t₂

After 9 months the value of both the model will be the same.

For long term payment, model B will be of less value.

Explanation:

Model A was an LG Electronics 25 cubic feet fridge that would cost $1399.99 initially and the monthly electric cost would be about $92 per month.

So, the price after t₁ months will be

C₁ = 1399.99 + 92t₁ ............ (1)

Model B, a Maytag 25 cubic feet refrigerator, was on sale for $1839.99 with a monthly electricity cost of about $43 per month.

Hence, the price after t₂ months will be

C₂ = 1839.99 + 43t₂ ............. (2)

Let after t months both the price be equal.

Hence, 1399.99 + 92t = 1839.99 + 43t

⇒ 49t = 440

⇒ t = 8.979 ≈ 9 months.

Therefore, for t more than 9 months say, 10 months, the price of the Model A = 1399.99 + 920 = $2319.99 and the price of the Model B = 1839.99 + 430 = $2269.99

Therefore, for long term payment, model B will be of less value. (Answer)