Question

Company A sells windows at a base cost of $30 and an additional cost of $2 per window. Company B sells windows at a base cost of $5 and an additional cost of $6 per window. What is the least number of windows that you would need to buy to have Company B be cheaper?

A) 6 windows
B) 8 windows
C) 10 windows
D) 12 windows

Answer 1

The least number of windows you would need to buy to have Company B be cheaper is B) 8 windows.

Step-by-step explanation:

To determine the least expensive option between Company A and Company B, we need to compare the total cost for each company based on the number of windows purchased.

Let x be the number of windows. The total cost for Company A is given by the equation C_A = 30 + 2x , and for Company B, it is C_B = 5 + 6x .

To find the number of windows where Company B is cheaper than Company A, we set the two costs equal to each other and solve for x :

30 + 2x = 5 + 6x

First, subtract 2x from both sides:

30 = 5 + 4x

Then, subtract 5 from both sides:

25 = 4x

Now, divide by 4:

x = 6.25

Since the number of windows must be a whole number, we round up to the nearest integer. Thus, x = 7 .

Now, we check the costs for both companies when x = 7 :

C_A = 30 + 2(7) = 44

C_B = 5 + 6(7) = 47

Next, we check the costs when x = 8 :

C_A = 30 + 2(8) = 46

C_B = 5 + 6(8) = 53

So, the least number of windows needed for Company B to be cheaper is 8 windows, Option B is correct.