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

let x be the number of mattresses to be cleaned. x is the variable that we will use in the equation.

Company A charges: 30x + 13 (Company A charges $30 per mattress and an additional $13 as service charges)

Company B charges: 28x + 15 (Company B charges $28 per mattress and an additional $15 as service charges)

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

for x = 4 mattresses

Company A charges: 30*4 + 13 = $133

Company B charges: 28*4 + 15 = $127

127 < 133 thus Company A charges less

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

for 7 mattresses

Company A charges: 30*7 + 13 = $293

Company B charges: 28*7 + 15 = $211

the money saved is the difference 293 - 211 = $82.