Question

Jake is comparing the prices of two laundry service companies. Company A charges $20 per load and an additional $8 as service charges. Company B charges $24 per load and an additional $4 as service charges.

Part A: Write an equation to represent each company's total charges for cleaning a certain number of loads of laundry. For both equations (one for Company A and one for Company B), define the variable used. (4 points)

Part B: Which company would charge less for 5 loads of laundry? Justify your answer. (3 points)

Part C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry? (3 points)

Answer 1

Part A: Write an equation to represent each company's total charges for cleaning a certain number of loads of laundry.
lets x = # of loads
Company A : 20x + 8
Company B: 24x + 4

Part B: Which company would charge less for 5 loads of laundry? Justify your answer. (3 points)

Company A : 20x + 8 = 20(5) + 8 = 100 + 8 = 108
Company B: 24x + 4 = 24(5) + 4 = 120 + 4 = 124

Company A charges $16 less than company B for 5 loads of laundry

Part C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry? (3 points)

Company A : 20x + 8 = 20(9) + 8 = 180 + 8 = 188
Company B: 24x + 4 = 24(9) + 4 = 216 + 4 = 220

220 - 188 = $32

You would save $32 by using the services of Company A instead of Company B to clean 9 loads of laundry

Answer 2

Part A:
Company A: Charges= $20x+$8
(I knew 20 was the coefficient for x instead of 8 because in the question it says $20 "per a load" which is a clue that it is multiplied by a variable. I knew that 8 did not come with a variable because it was describribed as a one time charge for using the laundry service)

Company B: Charges= $24x+$4

the variable used for both equations was "x".
variable x= number of loads of laundry that Jake has.





Part B: which company would charge less for 5 loads of laundry? (so, when x=5)

Comp. A: C= 20x+8
C= 20(5)+ 8
C= 100 +8
C= $108

For company A, the total charges for 5 loads is $108.

Comp. B: C= 24x +4
C=24(5)+4
C=120+4
C=$124

For compamy B, the total charges for five loads add up to $124. COMPANY A CHARGES LESS FOR 5 LOADS OF LAUNDRY BECAUSE 124>108.



Part C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry? (so, when x=9, what is Cb-Ca = to?)

Comp.A: C=20x+8
C=20(9)+8
C=180 + 8
Ca=$188

Comp. B: C=24x+4
C=24(9)+4
C=216+4
Cb=$220


Final answer part C:
Cb-Ca= answer
220-188=$32

$32 are saved by using Company A rather than Company B.