Question

Can you help me solve 10 a and b

Answer 1

10.

a) x- is the time after which the total cost is the same.

24 + 99x - is the cost in the dealership

45 + 89x is the cost at the local mechanic

24 +99x = 45 + 89x

99x - 89x = 45 - 24

10x = 21

x= 2.1 (hours)

b) 24 +99x < 45 + 89x

x< 2.1

The repairs cost less in dealership when work takes less than 2.1, and the dealership is better, because the cost of parts is less in the dealership.

Answer 2

Let h = number of hours. The total cost of the repair at the dealer and at the local mechanic is calculated the same way. It is the price of the parts plus the cost of labor. The cost of labor is the number of hours multiplied by the labor cost per hour.

Part a)

Dealership:

cost of parts = 24

cost of labor = 99h

total cost = 99h + 24

Local mechanic:

cost of parts = 45

cost of labor = 89h

total cost = 89h + 45

The only variable we have is h, the number of hours. We set the total costs equal and solve for h, the number of hours. That will tell us the number of hours for which the total costs are the same.

99h + 24 = 89h + 45

10h = 21

h = 2.1

Answer for a): 2.1 hours

Part b)

We want to know the number of hours for which the dealership costs less. We use the expressions for costs, but now we set the dealership as costing less than the local dealer. We set up an inequality and solve for h.

99h +24 < 89h + 45

10h < 21

h < 2.1

Answer for b): For less than 2.1 hours of labor, the dealership costs less.

Explanation: The dealership has a lower fixed cost since the parts cost less at the dealership. The labor costs more per hour at the dealership. If the repair took no time at all, the dealership would cost only $24 vs $45 at the local mechanic, so the total bill would be $21 less at the dealership. For every hour of labor at the dealership, you pay $10 more in labor costs, so after 2.1 hours, the two costs are the same, and for more than 2.1 hours, the dealership costs more.