My son need help with this maths

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 W=78b+8840 gives the total weight of the truck if it is carrying  boxes. Suppose the truck is not legally allowed to weigh more than 13200 pounds.

1. Will your rental truck be able to legally carry the load of 60 boxes? Explain.
2. If not, determine the maximum number of boxes the rental truck can legally carry.

Answer 1

W(b) = 78b + 8840 defines a linear relationship between number of boxes loaded on the truck and the total weight of the truck (where b is the number of boxes loaded).

Note that when b = 0 we have:

W(0) = 78(0) + 8840 = 8840 (which is the weight of the empty truck).

As we load boxes the weight of the truck increases by 78 pounds for each box loaded.

W(1) = 78(1) + 8840 = 8918

W(2) = 78(2) + 8840 = 8996

...

How about 50 boxes:

W(50) = 78(50) + 8840 = 12740 (still within the legal limit).

What happens if all 60 boxes are loaded?

W(60) = 78(60) + 8840 = 13520 (over the legal limit), so the answer to part 1, the truck cannot legally carry all 60 boxes.

To determine how many boxes the truck can carry:

78b + 8840 ≤ 13200

78b ≤ 4360

b ≤ 4360/78 ≤ 55.9 (that means max number of boxes is 55--since you cannot load a fraction of a box).

Note:

W(55) = 78(55) + 8840 = 13130

but,

W(56) = 78(56) + 8840 = 13208 (8 lbs too much).

Here is a Desmos graph that depicts this linear relationship (using x for the independent variable instead of "b").

desmos.com/calculator/hltziacpop