Emily needs to purchase a new air conditioner for the office. Model 1600A costs $950 to purchase and $32 per month to operate

Question

Emily needs to purchase a new air conditioner for the office. Model 1600A costs $950 to purchase and $32 per month to operate. Model 6070B, a more efficient unit, costs $1275 to purchase and $22 per month to operate.
a) After how many months will the total cost of both units be equal?
b) Which model will be the more cost effective if the life of both units is guaranteed for 10
years?

Answer 1

Let total cost = purchase price + monthly operating cost × months

Model 1600A:

C = 950 + 32m

Model 6070B:

C = 1275 + 22m

Set them equal:

950 + 32m = 1275 + 22m

10m = 325

m = 32.5

a) Answer:

The total cost of both units will be equal after 32.5 months.

b) For 10 years

10 years = 120 months

Model 1600A:

950 + 32(120) = 950 + 3840 = 4790

Model 6070B:

1275 + 22(120) = 1275 + 2640 = 3915

Answer:

After 10 years, Model 6070B is more cost effective.

Model 1600A is cheaper to buy at first, but it costs more each month to run. Model 6070B costs more upfront, but saves $10 per month in operating cost, so over a long time it becomes the cheaper choice.

Answer 2

32m + 950 = 22m + 1275

 

Solve for m.

 

32(10) + 950

 

22(10) + 1275

 

Which is less?

 

You got this!