Question

Ms. Mbariket needs to have her car repaired but does not want to spend more than $375 for the repairs. The mechanic says that the part needed for the repair will cost $100, and the labor will cost an additional $40 per hour. Which inequality below represents the greatest number of hours the mechanic can work without exceeding Ms. Mbariket's budget?

a. 40 + 100x < 375
b. 100 + 40x < 375
c. 140x < 375
d. 100 + 40.2x > 375

Answer 1

The correct inequality that represents the greatest number of hours the mechanic can work without exceeding Ms. Mbariket's budget of $375 for her car repairs is 100 + 40x < 375.

Step-by-step explanation:

Ms. Mbariket needs to have her car repaired but does not want to spend more than $375 for the repairs. We are tasking with identifying the inequality that represents the greatest number of hours the mechanic can work without exceeding this budget.

The cost of the part needed for the repair is $100, and the mechanic charges $40 per hour for labor. Thus, the total cost of the repair will be the cost of the part plus the labor cost, which is calculated by multiplying the number of hours worked (x) by the hourly labor charge ($40). Therefore, the inequality that represents the cost of the repair is:

Total Cost = Cost of Part + (Hourly Labor Charge × Number of Hours Worked)

100 + 40x (Total Cost must be less than or equal to $375)

So the correct inequality is:

100 + 40x < 375

This inequality will determine the maximum number of hours that the mechanic can work without surpassing Ms. Mbariket's budget of $375 for her car repairs.