Question

You are loading a rental truck with 78-pound boxes and have 60 boxes to load. If the empty truck weighs 8840 pounds, then the equation gives the total weight of the truck =78+8840 if it is carrying boxes.

Suppose the truck is not legally allowed to weigh more than 13200 pounds. Will your rental truck be able to legally carry the load of 60 boxes? Explain.

If not, determine the maximum number of boxes the rental truck can legally carry.

Answer 1

55 boxes

Explanation:

Using Linear Equations:

The linear equation provided is:
`y=78x+8840` and since we want to check if we can carry 60 boxes, we just need to weight by substituting in "60" as x and then comparing that to the limit of 13200 pounds.

`y = 78(60)+8840\\\\y=4680+8840\\\\y=13,520`

This of course is over the limit of 13200 pounds but we can set up an inequality and solve for "x"

`78x+8840 < 13200`

From here we subtract 8840 from both sides

`78x < 4,360`

Now divide both sides by 78

`x < 55.89`

now of course we can't have 55.89 boxes, so we want to round down as we can't have 56 boxes as that would go over the limit, but we can have 55 boxes.