Question

trainload of cars and trucks is in route to an auto dealer for whom you work. Before they arrive the dealers receives and invoice showing 160 vehicles but the part of the invoice showing how many of each kind of the vehicle has been torn off. Your boss needs to know how many of each before they arrive. The invoice shows a total mass of 182,800 kilograms of vehicles. Each truck is 1,400 kilograms and each card is 1,000 kilograms. How many of each kind are there.

Please explain this to me

Answer 1

Explanation:

Let the number of cars be c, trucks be t.

The total number of vehicles = 160,

c+t =160

Now how to show the mass of vehicles?

If there are c number of cars, with each car being 1000kg, the total weight of all the cars would be 1000c kg. With the same logic, the total weight of all the trucks would be 1400t kg.

If they all weigh 182,800kg together,

1000c + 1400t = 182 800

Looking at both of the equations now:

c+t =160

1000c + 1400t = 182 800

We have to make one of them cancel out the other, so:

1. Mutiply both sides of c+t=160 by 1000, you get

1000c + 1000t = 160 000

2. Subtract this equation from the second one above,

1000c + 1400t - (1000c + 1000t) = 182 800 - 160 000

1000c - 1000c + 1400t - 1000t = 22800

400t = 22800

t = 57

3. Substitute t= 57 into the first equation, c + t = 160,

c= 160-57 = 103

So you have 57 trucks, 103 cars.