Question

Maria is comparing the prices of two window cleaning companies. Company A charges $6 per window and an additional $12 as service charges. Company B charges $5 per window and an additional $15 as service charges. Part A: Write equations to represent Company A's and Company B's total charges for cleaning a certain number of windows. Define the variable used in the equations. (4 points) Part B: Which company would charge less for cleaning 8 windows? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company B instead of Company A to clean 6 windows? (3 poi

Answer 1

hint: first equation y=6x+12 gives the charge (y) for x windows

Answer 2

I'm still clueless :( Do I divide?

Answer 3

Here's what I submitted:

Part A (Company A)-
We know that Company A charges $6 per window, and an additional $12 as service charges. First we need to set up an equation and then define the variables. Equation below:

6w + 12 = t

W is the number of windows that are being cleaned. T represents the total cost that needs to be payed.

A Run-down of how I formed this equation:
I was told that the company charges $6 per window...and the key word in that sentence is "per". This word indicates multiplication. So, 6 times w is how I decided to display this information. After you multiply these two values you need to add 12 to the product. We do this because we were told that an additional (additional is the key word for addition) $12 is being tagged onto the bill as a service fee. After you've done this you've solved the equation!

Solving for t (Company A)-
You've decided that you want to have 8 windows cleaned. So, using the equation we've formed we can solve for (t), or the total cost.

(6*8) + 12 = t (multiply to clear the parenthesis)
48 + 12 = t (add the two values to solve for t)
60 = t (your answer)

You've finished solving the equation and are aware of how much you would owe the company.

Part A (Company B)-
We know that this company charges $5 per window and an additional $15 service fee. We can use the same equation for this company as we did Company A. All we have to do is tweak the values. Equation below:

5w + 15 = t

W is the number of windows you are having cleaned. T is the total cost that needs to be payed.

A Run-down of how I formed this equation:
I was told that the company charges $5 per window...and the key word in that sentence is "per". This word indicates multiplication. So, 5 times w is how I decided to display this information. After you multiply these two values you need to add 15 to the product. We do this because we were told that an additional (additional is the key word for addition) $15 is being tagged onto the bill as a service fee. After you've done this you've solved the equation!

Solving for t (Company B)-
You've decided that you want to have 8 windows cleaned. So, using the equation we've formed we can solve for (t), or the total cost.

(5*8) + 15 = t (multiply to clear the parenthesis)
40 + 15 = t (add the two values to solve for t)
55 = t (your answer)

You've finished solving the equation and are aware of how much you would owe the company.

Part B-
Company B would be less expensive to have 8 windows cleaned as opposed to Company A. I know this because I've formed my equation, I've identified my variables, I've substituted my variable with its known value, and finally I solved the equation for both companies conditions.
Company B charges $55 to have 8 windows cleaned. Whereas Company A would charge $60 to have 8 windows cleaned.

Part C-
To figure this out we simply solve the equation for both companies condition.
Company A:
6w + 12 = t
(6*6) + 12 = t
36 + 12 = t
48 = t

Company B-
5w + 15 = t
(5*6) + 15 = t
30 + 15 = t
45 = t

We know that Company A would charge $48 to have 6 windows cleaned, and Company B would charge $45 to have 6 windows cleaned. So the difference (key word for subtract) between these two values is 3. There's a $3 difference, or in other words you would be saving $3 if you went with Company B.