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 equations to represent Company A's and Company B's total laundry charges for a certain number of loads. Define the variable used in the equations. (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

This is a system of linear equations.

Part A: 

Be:

L: Load of laundry
T: Total laundry charges

Equations:

Company A: $T=20L+8$
Company B: $T=24L+4$

Part B

To answer this question we need to substitute the load into each equation and to find which company is cheaper.

Company A: $T=20(5)+8=108$
Company B: $T=24(5)+4=124$

Company A charges less for 5 loads of laundry.

Part C

To answer this question we need to substitute the load into each equation and to find the difference between Company B and A that is the saved money.

Company A: $T=20(9)+8=188$
Company B: $T=24(9)+4=220$

The money saved is the difference between Company B and A:

$\Delta=220-188=\ 32$

Answer 2

Let Y be the number of loads Jake takes to the laundry.

Part A
Cost of company A. (20×Y) + 8 = 20Y + 8
Cost of company B: (24×Y) + 4 = 24Y + 4
Y is the number of loads taken to the laundry. 

Part B
For Y = 5
Cost of company A =(20×5) + 8 = $108
Cost of company B = (24×5) + 4 = $124. 

From the calculation above, it is verified that for 5 loads company A would spend less. 

Part C
For 9 loads the charges of the 2 companies are:
Company A =(20×9) +8 = $188
Company B = (24×9) + 4 = $220

By using services for company A Jake would save;

$220 - #188 = $32