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Math  /  Algebra

Question6. A rental car agency charges $240\$ 240 per week plus $0.25\$ 0.25 per mile to rent a car. The charge for a minivan is $180\$ 180 per week plus $0.40\$ 0.40 per mile. After how many miles is the total charge for each vehicle the same?

Studdy Solution

STEP 1

1. The rental car agency charges $240\$240 per week plus $0.25\$0.25 per mile for a car.
2. The charge for a minivan is $180\$180 per week plus $0.40\$0.40 per mile.
3. We need to find the number of miles after which the total charge for each vehicle is the same.

STEP 2

1. Define variables for the problem.
2. Write expressions for the total cost of renting each vehicle.
3. Set the expressions equal to each other to find the number of miles.
4. Solve the equation for the number of miles.

STEP 3

Define variables for the problem.
Let m m represent the number of miles driven.

STEP 4

Write expressions for the total cost of renting each vehicle.
For the car, the total cost is: Ccar=240+0.25m C_{\text{car}} = 240 + 0.25m
For the minivan, the total cost is: Cminivan=180+0.40m C_{\text{minivan}} = 180 + 0.40m

STEP 5

Set the expressions equal to each other to find the number of miles.
240+0.25m=180+0.40m 240 + 0.25m = 180 + 0.40m

STEP 6

Solve the equation for the number of miles.
First, subtract 0.25m 0.25m from both sides: 240=180+0.15m 240 = 180 + 0.15m
Next, subtract 180 180 from both sides: 60=0.15m 60 = 0.15m
Finally, divide both sides by 0.15 0.15 : m=600.15 m = \frac{60}{0.15} m=400 m = 400
The total charge for each vehicle is the same after 400 \boxed{400} miles.

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