Answer :

The U-Drive Rent-A-Truck company can buy 160 vans, 80 small trucks, and 20 large trucks.

1. Define Variables:

Let "x" be the number of small trucks.

2. Formulate Equations:

Given:

- Total budget: $14 million

- Cost per vehicle: $45,000 for vans, $70,000 for small trucks, $60,000 for large trucks

- Total number of vehicles: 260

- Number of vans needed: Twice the number of small trucks

We can set up the following system of equations:

Total cost equation:

45000(2x) + 70000x + 60000y = 14000000

Total number of vehicles equation:

x + 2x + y = 260

3. Solve the System of Equations:

We have the system of equations:

- 16x + 6y = 1400

- 3x + y = 260

4. Solve the System of Equations:

Using the elimination method:

- Multiply the second equation by 6 to match the coefficient of "y":

- (16x + 6y = 1400)

- (18x + 6y = 1560)

- Subtract the second equation from the first:

- -2x = -160

- x = 80

Substitute x = 80 into the second equation:

- 3(80) + y = 260

- 240 + y = 260

- y = 20

5. Find the Number of Vans:

Number of vans = 2x = 2(80) = 160

6. Result:

The company can buy 160 vans, 80 small trucks, and 20 large trucks.

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Question

The U-Drive Rent-A-Truck company plans to spend $14 million on 260 new vehicles. Each commercial van will cost $45,000, each small truck $70,000, and each large truck $60,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? Vans?, Small trucks?, and large trucks?

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Rewritten by : Barada