A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pound...

Question

A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45

 pounds each, and the small boxes weigh 35

 pounds each. There are 115

 boxes in all. If the truck is carrying a total of 4575

 pounds in boxes, how many of each type of box is it carrying? 

Answer 1

Let l represent the number of large boxes and s represent the number of small boxes.

There are 115 boxes in all, so l + s = 115.

Large boxes weigh 45 pounds, so the total weight of all the large boxes is 45l.

Small boxes weigh 35 pounds, so the total weight of all the small boxes is 35s.

The total weight of all the boxes, large and small, is 45l + 35s.

The total weight is 4575 pounds, so 45l + 35s = 4575.

Now you have a system of 2 variables in 2 equations:

l + s = 115

45l + 35s = 4575

so you can solve by substitution.

l + s = 115, so l = 115 - s and you can substitute that into the second equation.

45(115 - s) + 35s = 4575

5175 - 45s + 35s = 4575

5175 - 10s = 4575

- 10s = - 600

s = 60

Remember, s is the number of small boxes, so there are 60 small boxes.

Substitute 60 for s in the first equation.

l + 60 = 115

l = 55

Remember, l is the number of large boxes, so there are 55 large boxes.