Question

The​ u-drive rent-a-truck company plans to spend ​$10 million on 260 new vehicles. each commercial van will cost ​$25 comma 000 ​, each small truck ​$50 comma 000 ​, and each large truck  ​$50 comma 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

Answer: They would buy 130 vans, 65 small trucks and 65 large trucks

Explanation: Budget has been given as $10,000 and the company needs up to 260 vehicles, commercial vans($25000), small trucks ($50000) and large trucks ($50000). They need twice as many vans as small trucks which means for every small truck purchased, they would purchase two commercial vans, or ratio 2:1 for the ratio of commercial vans to small trucks. The cost of the small truck is the same as the cost of the large truck. Therefore the ratio would be 2:1:1, for the ratio of commercial vans to small trucks to large trucks.

The number of commercial vans to be purchased therefore is derived as

2/4 = x/260

(2 x 260)/4 = x

520/4 = x

130 = x

The number of vans to be purchased is 130 and this is twice the number of small trucks which means small trucks purchased would be 130 divided by 2 which equals 65, and large trucks also would be 65 making a total of 260 vehicles.

Answer 2

Answer: 120 commercial vans, 60 small trucks, and 80 large trucks

Explanation: First, we will define the variables that we need to solve the problem. In this case the question is, how many of each type of vehicle, so let

V = number of vans

S = number of small trucks

L = number of large trucks

Next, we will translate the words in the problem into mathematical statements that we can use to solve the problem, thus:

"twice as many vans as small trucks" means that:

V = 2*S

"260 new vehicles" means that:

V + S + L = 260

The last part is the cost equation which is a little more complicated:

25000*V + 50000*S + 50000*L = 10,000,000

Divide both sides of this equation by 1000, we have:

25*V + 50*S + 50*L = 10000

We start with the simplest one:

V = 2*S.

This means that wherever we see a V in the other 2 equations we can replace it with 2*S, which will leave us with 2 equations in 2 unknowns

(2*S) + S + L = 260 ==> 3*S + L = 260

25*(2*S) + 50*S + 50*L = 10000

==> 100*S + 50*L = 10000

Now we can solve the top equation for L to get L = 260 - 3*S

and substitute this value for L into the bottom equation

100*S + 50*(260 - 3*S) = 10000

100*S + 13000 - 150*S = 10000

-50*S = -3000

S = 60

Once we have one of the answers then plug in back in to previous equations to find the others

L = 260 - 3*S = 260 - 3*(60)

= 260 - 180 = 80

V = 2*S = 2*(60) = 120

So they can buy 120 commercial vans, 60 small trucks, and 80 large trucks