Question

The greatest weight a moving truck can carry is 1,600 pounds. The truck is loaded with a

piano that weighs 400 pounds. Boxes that weigh 50 pounds each will also be loaded into the
truck.
Which inequality represents all possible values of x, the number of these boxes that can be
loaded into the moving truck?

Answer 1

The inequality representing the maximum number of boxes that can be loaded into the truck without exceeding the weight limit is x <= 24.

Step-by-step explanation:

The greatest weight that the moving truck can carry is 1,600 pounds. There is a piano that weighs 400 pounds already loaded onto the truck. We want to find out all the possible values of x, the number of 50-pound boxes that can be added without exceeding the truck's maximum capacity. The weight of the boxes can be represented as 50x pounds, where x is the number of boxes.

So, we have the piano's weight + the total weight of the boxes which is equal to 400 + 50x pounds. This total weight must be less than or equal to the truck's maximum capacity, 1,600 pounds, which gives us the inequality:

400 + 50x <= 1,600

To find the solution for x, we need to subtract the weight of the piano from both sides of the inequality:

50x <= 1,600 - 400
50x <= 1,200

Then divide both sides by 50 to solve for x:

x <= 24

Therefore, the inequality that represents all possible values of x, the number of 50-pound boxes that can be loaded into the moving truck, is x <= 24.