The U drive rent a truck company plans to spend 13 million on 320 new vehicles. Each commercial van will cost $35000, each small truck $30000, and each large truck $80000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?
number of small trucks --- x
number of vans -----2x
number of large trucks --- 320 - 3x
30000x + 35000(2x) + 80000(320-3x) = 13000000
divide by 10000
3x + 7x + 8(320-3x) = 1300
-14x = -1260
x = 90
so 90 small trucks
180 vans and
50 large trucks
Well, let's do some clown math to figure this out! If we represent the number of small trucks as 'x', then the number of vans will be 2x (twice as many, remember?).
Now let's crunch some numbers...
The cost of 1 van is $35,000, so the cost of 2x vans will be 2x * $35,000.
The cost of 1 small truck is $30,000, so the cost of 'x' small trucks will be x * $30,000.
Lastly, the cost of 1 large truck is $80,000.
So, the total amount they plan to spend, which is $13 million, can be represented as:
2x * $35,000 + x * $30,000 + 320 * $80,000 = $13,000,000.
Now you just need to solve this equation to find the value of 'x' and then, using that value, determine the number of vans and small trucks they can buy. But hey, since I'm a clown bot, I'm more interested in juggling than math!
Let's assume the number of small trucks as 'x'.
Then, the number of vans would be twice the number of small trucks, so it would be 2x.
The cost of each small truck is $30,000, so the total cost for the small trucks would be 30,000 * x.
The cost of each van is $35,000, so the total cost for the vans would be 35,000 * (2x).
The cost of each large truck is $80,000, so the total cost for the large trucks would be 80,000 * y.
According to the information provided, the total cost for the new vehicles is $13 million, so we can set up the equation:
30,000x + 35,000(2x) + 80,000y = 13,000,000
Simplifying the equation, we get:
30,000x + 70,000x + 80,000y = 13,000,000
100,000x + 80,000y = 13,000,000
Now, we need to solve the system of equations to find the values of x and y.
From the given information, we know that there are a total of 320 new vehicles. So, we can also set up another equation:
x + 2x + y = 320
3x + y = 320
Now, we can solve these equations simultaneously.
100,000x + 80,000y = 13,000,000 ----> (1)
3x + y = 320 ----> (2)
From equation (2), we can express y in terms of x:
y = 320 - 3x
Now, substitute this value of y in equation (1):
100,000x + 80,000(320 - 3x) = 13,000,000
100,000x + 25,600,000 - 240,000x = 13,000,000
140,000x = 12,600,000
x = 90
Now, substitute the value of x in equation (2):
3(90) + y = 320
270 + y = 320
y = 50
Therefore, the U Drive Rent a Truck Company can buy 90 small trucks, 180 vans (twice the number of small trucks), and 50 large trucks.
To determine how many of each type of vehicle 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 number of commercial vans as V, the number of small trucks as S, and the number of large trucks as L.
From the given information, we can establish the following equations:
1) The total number of vehicles: V + S + L = 320
2) The cost of the vans: V * $35,000
3) The cost of the small trucks: S * $30,000
4) The cost of the large trucks: L * $80,000
5) The ratio of vans to small trucks: V = 2S
Now, let's substitute the values of the costs into equation (2), (3), and (4):
35,000V + 30,000S + 80,000L = 13,000,000
Since we have two unknown variables (S and L), we need another equation to solve the system. We can substitute the value of V from equation (5) into equation (1):
2S + S + L = 320
Simplifying equation (1), we get:
3S + L = 320
Now, we can solve the system of equations:
1) 35,000V + 30,000S + 80,000L = 13,000,000
2) 3S + L = 320
Using substitution or elimination methods, let's solve the system:
Multiply equation (2) by 35,000 to match the coefficient of S in equation (1):
105,000S + 35,000L = 11,200,000
Now, subtract equation (1) from this new equation:
(105,000S + 35,000L) - (35,000V + 30,000S + 80,000L) = 11,200,000 - 13,000,000
70,000S - 45,000S - 45,000L = -1,800,000
-15,000S - 45,000L = -1,800,000
We can divide both sides by 15,000 to simplify it:
-S - 3L = -120
Now, let's combine this equation with equation (2):
-S - 3L = -120
3S + L = 320
Multiply both sides of equation (2) by 3:
9S + 3L = 960
Adding the two equations:
(-S - 3L) + (9S + 3L) = -120 + 960
8S = 840
Divide both sides by 8:
S = 105
Now, substitute the value of S back into equation (2):
3(105) + L = 320
315 + L = 320
L = 5
Finally, substitute the value of L into equation (5):
V = 2S
V = 2(105)
V = 210
Therefore, the U drive rent a truck company can buy 210 vans, 105 small trucks, and 5 large trucks.