A solar energy company offers two payment plans for installing solar panels. Under Plan A,… — SAT

A solar energy company offers two payment plans for installing solar panels. Under Plan A, the customer pays a one-time installation fee of $1,200 and a monthly maintenance fee of$ 25. Under Plan B, there is no installation fee, but the customer pays a monthly maintenance fee of $45 for the first 12 months, and$ 35 per month for each month thereafter. If a customer chooses Plan A, after how many months of service will the total cost of Plan A be exactly equal to the total cost of Plan B?

A
24
B
66
108Answer
D
132

Answer

The correct answer is 108 months.

The correct answer is 108. Setting the total cost of Plan A,

1200 + 25m

, equal to the total cost of Plan B,

45(12) + 35(m-12)

, yields the linear equation

1200 + 25m = 120 + 35m

. Isolating

m

by subtracting

25m

and

120

from both sides gives

10m = 1080

, which simplifies to

m = 108

Step-by-Step Solution

Set up the total cost expression for Plan A.

\text{Cost}_A = 1200 + 25m

Plan A has a fixed setup fee of

1,200 plus a recurring cost of

25 for each of the

m

months.

Set up the total cost expression for Plan B, assuming the number of months

m > 12

\text{Cost}_B = 45(12) + 35(m - 12) = 540 + 35m - 420 = 120 + 35m

Plan B charges

45 per month for the first 12 months and

35 per month for the remaining

m - 12

months.

Equate the two expressions and solve for

m

1200 + 25m = 120 + 35m \Rightarrow 1080 = 10m \Rightarrow m = 108

Setting the two costs equal allows us to isolate the variable

m

by subtracting

25m

and

120

from both sides.

Key Concept

Formulating and solving multi-step linear equations in one variable from real-world word problems.

Estimated Time:2m 30s

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