Your factory makes tires. It costs you $175,000 to pay for the lease each year. The cost to make a tire, including labor and materials, is $53 per tire.

Write the equation of the line that represents the total cost $ C $ as a function of the number of tires $ x $ produced.

A. [tex]C = 175,000 + 53x[/tex]
B. [tex]C = 53x + 175,000[/tex]
C. [tex]C = 175,000x + 53[/tex]
D. [tex]C = 53 + 175,000x[/tex]

The correct equation representing the total cost of producing tires, factoring in both the fixed lease and variable production costs per tire, is C = 53x + 175,000. So the correct answer is option(b).

Explanation:

The question pertains to finding the correct equation that represents the total cost of producing tires in a factory, taking into account both the fixed lease cost and the variable production cost per tire. Given are: the yearly lease cost of $175,000 and the cost to make each tire at $53. The correct representation of the total cost (C) as a function of the number of tires produced (x) is C = 53x + 175,000.

This equation aligns with option b) C = 53x + 175,000, where 53x represents the variable production costs for x number of tires, and 175,000 is the fixed annual lease cost. The addition of these two amounts gives us the total cost of producing x tires in a year. Therefore, as the number of tires produced increases, the variable part of the total cost rises, whereas the fixed cost remains constant, irrespective of the production volume.