Borox is loading a freight elevator with 12 boxes: 4 small, 5 medium, and 3 large. A small box and medium box together weigh 20 pounds; a medium box and a large box together weigh 28 pounds, and a large box with a small box weighs 24 pounds. What is the total weight of the 12 boxes?

140 pounds

Step-by-step explanation:

let s == small box

m = medium box

= large box

the following 3 equations can be derived from the question

s + m = 20 equation 1

m + l = 28  equation 2

l + s = 24  equation 3

make m the subject of the formula in equation 1 and 2

m = 20 - s  equation 4

m = 28 - l  equation 5

equate equation 4 and 5

20 - s = 28 - l

l - s = 8  equation 6

solve equation 3 and 6 using simultaneous equation

l + s = 24  equation 3

l - s = 8  equation 6

subtract equation 6 from 3

2s = 16

s = 8

substitute for s in equation 1

8 + m = 20

m = 12

substitute for m in equation 2

12 + l = 28

l = 16

total weight = (4 x 8) + (5 x 12) + (16 x 3) = 140 pounds