The U-Drive Rent-A-Truck company plans to spend $8 million on 280 vehicles. Each commercial van will cost $25,000, each small truck $30,000, and each large truck $40,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?'

Question

The U-Drive Rent-A-Truck company plans to spend $8 million on 280 vehicles. Each commercial van will cost $25,000, each small truck $30,000, and each large truck $40,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?'

Answer 1

Let's assign variables to each type of vehicle:

Let V = number of vans
Let S = number of small trucks
Let L = number of large trucks

According to the given information, we have the following equations:

1. V + S + L = 280 (Total number of vehicles should equal 280)
2. V = 2S (Twice as many vans as small trucks)
3. $25,000V + $30,000S + $40,000L = $8,000,000 (Total cost of vehicles should equal $8 million)

To solve this system of equations, we can use a combination of substitution and solving for variables.

Let's start with equation 2 and substitute V in equation 1:

2S + S + L = 280
3S + L = 280 (Equation A)

Substituting V in equation 3:

$25,000(2S) + $30,000S + $40,000L = $8,000,000
$50,000S + $30,000S + $40,000L = $8,000,000
$80,000S + $40,000L = $8,000,000 (Equation B)

Now, let's express equation A in terms of L:

L = 280 - 3S

Substitute this value of L in equation B:

$80,000S + $40,000(280 - 3S) = $8,000,000
$80,000S + $40,000(280) - $120,000S = $8,000,000
$200,000S = $8,000,000 - $40,000(280)
$200,000S = $8,000,000 - $11,200,000
$200,000S = -$3,200,000
S = -($3,200,000 / $200,000)
S = -16

Since the number of vehicles cannot be negative, we can conclude that there is no solution within the given constraints.

Answer 2

To determine the number of each type of vehicle that the U-Drive Rent-A-Truck company can buy, we need to set up a system of equations based on the given information.

Let's denote the following variables:
V = Number of commercial vans
S = Number of small trucks
L = Number of large trucks

According to the given information:
1. The company plans to spend $8 million on vehicles. The total cost (C) can be calculated as:
C = 25000V + 30000S + 40000L

2. The company plans to buy a total of 280 vehicles:
V + S + L = 280

3. The company needs twice as many vans as small trucks:
V = 2S

Now we can solve this system of equations to find the values of V, S, and L.

Substitute equation 3 into the equation 2:
2S + S + L = 280
3S + L = 280 ----(4)

Substitute equations 3 and 4 into the equation 1 to find the total cost (C):
C = 25000(2S) + 30000S + 40000L
C = 50000S + 30000S + 40000L
C = 80000S + 40000L ----(5)

Now we have two equations: equation 3 and equation 5:
80000S + 40000L = 8,000,000 ----(6)
3S + L = 280 ----(7)

By solving equations 6 and 7 simultaneously, we can find the values of S (small trucks) and L (large trucks).

Answer 3

number of small trucks --- x

number of vans ----- 2x
number of large trucks = 280 - 3x

30,000x + 25,000(2x) + 40,000(280-3x) = 8,000,000
divide by 5000
6x + 10x + 8(280-x) = 1600

carry on