this is another from a different section can you show me how to solve it.

An electronics company produces three
models of stereo speakers, models A, B, and C, and can
deliver them by truck, van, or station wagon. A truck holds
2 boxes of model A, 2 of model B, and 3 of model C. A van
holds 3 boxes of model A, 4 boxes of model B, and 2 boxes
of model C. A station wagon holds 3 boxes of model A,
5 boxes of model B, and 1 box of model C.
a. If 25 boxes of model A, 33 boxes of model B, and
22 boxes of model C are to be delivered, how many vehicles
of each type should be used so that all operate at full
capacity?
b. Model C has been discontinued. If 25 boxes of model A
and 33 boxes of model B are to be delivered, how many
vehicles of each type should be used so that all operate at
full capacity?

To solve this problem, we need to use a system of equations to represent the given information and then solve for the number of vehicles of each type. Let's break it down step by step:

a. To find how many vehicles of each type should be used when all operate at full capacity, we need to determine the number of vehicles required to transport the given number of boxes of each model.

Let's represent the number of vehicles of each type as follows:
Let x = number of trucks
Let y = number of vans
Let z = number of station wagons

Now, let's create equations based on the given information:

For model A:
Each truck holds 2 boxes of model A, so the number of trucks required is given by: x = (number of boxes of model A) / 2

For model B:
Each van holds 4 boxes of model B, so the number of vans required is given by: y = (number of boxes of model B) / 4

For model C:
Each station wagon holds 1 box of model C, so the number of station wagons required is given by: z = (number of boxes of model C) / 1

The total number of boxes for each model must be the same as the total number of boxes given in the problem.

Therefore, we create equations based on the given information:

x + y + z = total number of vehicles
2x + 3y + 3z = 25 (for model A)
2x + 4y + 5z = 33 (for model B)
3x + 2y + z = 22 (for model C)

Now, we have a system of equations that we can solve simultaneously.

b. We can approach Part B of the problem in the same way, but with the given information modified to reflect the discontinuation of model C. The new set of equations would be as follows:

x + y = total number of vehicles
2x + 3y = 25 (for model A)
2x + 4y = 33 (for model B)

Solving these systems of equations will give us the values of x, y, and z (or x and y in the case of Part B), representing the number of vehicles of each type required to transport the given number of boxes while operating at full capacity.