A train load of cars and trucks is en route to an automobile dealer for whom you work. Before they arrive, the dealer receives an invoice showing a total of 160 vehicles. Unfortunately, the part of the invoice showing how many of each kind of vehicles has been torn off and lost. The dealer need to know how many of each there will be before they arrive. Since you know algebra, you can save the day.

Question

A train load of cars and trucks is en route to an automobile dealer for whom you work. Before they arrive, the dealer receives an invoice showing a total of 160 vehicles. Unfortunately, the part of the invoice showing how many of each kind of vehicles has been torn off and lost. The dealer need to know how many of each there will be before they arrive. Since you know algebra, you can save the day.

Answer 1

1) x+y=160

2) 1400x+1000y=182,800

Set up an elimination equation. Solve for one variable. Finally plug in to equation 1 or 2 to get the other variable.

Answer 2

To solve this problem using algebra, we'll set up a system of equations.

Let's call the number of cars C and the number of trucks T.

From the information given, we know that:

C + T = 160 (Equation 1 - Total vehicles)

However, we don't know the individual values of C and T yet, so we need another equation to solve for them.

To create the second equation, we need more information. If we knew the total number of wheels on the train, we could use that to determine the number of cars and trucks since cars have 4 wheels and trucks have 18 wheels. However, since we don't have that information, we'll need to use a different approach.

We can make an assumption that each vehicle on the train has the same number of wheels. Let's say each vehicle has W wheels. Following this assumption, the total number of wheels on the train would be 160W.

Again, we don't know the exact value of W, so we still need more information or make another assumption.

Assuming that each car has 4 wheels and each truck has 18 wheels, we can write another equation based on the total number of wheels:

4C + 18T = 160W (Equation 2 - Total wheels)

Now we have a system of equations, Equation 1 and Equation 2, that we can solve simultaneously to find the values of C and T.

To solve the system of equations, we have a few options. One popular method is substitution. Here's a step-by-step guide to solving the system using substitution:

1. Solve Equation 1 for one variable in terms of the other.
C = 160 - T

2. Substitute the value of C from step 1 into Equation 2.
4(160 - T) + 18T = 160W

3. Simplify and solve for T.
640 - 4T + 18T = 160W
14T = 640 - 160W
T = (640 - 160W) / 14

Since we don't have the value of W, we can't determine the specific number of trucks (T) or cars (C). However, we can determine a relationship between them based on the given information.