Question

Jake is comparing the prices of two mattress cleaning companies. Company A charges $30 per mattress and an additional $13 as service charges. Company B charges $28 per mattress and an additional $15 as service charges.

Answer 1

Part A: Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable used in the equations.

Part B: Which company would charge less for cleaning 4 mattresses? Justify your answer.

Part C: How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses?

Answer 2

Company A charges $30 per mattress and an additional $13 as service charges.

if you have "x" mattresses, how much do they charge ?

Answer 3

30x

Answer 4

and an additional $13 as service charges.

Answer 5

so 30x + 13

Answer 6

yes

Answer 7

if we call the total amount charged f(x), you write
f(x) = 30x + 13

or, if you call the total amount charged "y", you write
y= 30x +13

now for B:

Company B charges $28 per mattress and an additional $15 as service charges.

Answer 8

28x + 15

Answer 9

so write it
y= 28x+15

where x is the number of mattresses, and y is the total cost

Answer 10

That is part A.

Part B: Which company would charge less for cleaning 4 mattresses? Justify your answer.
any idea how to do this ?

Answer 11

wait one minute though, this is how i wrote them:

Company A charges 30x + 13 for service charges
lets call the total amount charged f(x)
f(x) = 30x + 13


Company B charges 28x + 15 for service charges
lets call the total amount charged y
y = 28x + 15

Answer 12

ok, but
Company A charges 30x + 13 for service charges

does not read well. It sounds like the service charge is 30x+13
I would write
Company A charges 30x + 13 to clean x mattresses

Answer 13

ok i fixed it, ok now for part b?

Answer 14

yes. replace "x" with 4 in both equations and see which gives the smaller number (cheaper price)

Answer 15

f(4) = 30 * 4 + 13

or

30 * 4 + 13

Answer 16

you can simplify that to a single number

Answer 17

f(4) = 30 * 4 + 13 = 133

Answer 18

and how much does the other company charge to clean 4 mattresses?

Answer 19

y = 28 * 4 + 15 = 127

Answer 20

now you know the answer to part B, and why

Answer 21

ok and for part c
I do the same thing but with seven instead of 4