A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 12 large boxes and 2 small boxes has a total weight of 253 kilograms. A delivery of 3 large boxes and 5 small boxes has a total weight of 133 kilograms. How much does each type of box weigh?

Guest Aug 29, 2017

#1**+1 **

Let L be the weight of the large box and S be the weight of a small box

So.....we have this system

12L + 2S = 253

3L + 5S = 133

Looking at the second equation and multiplying both sides by 4, we have that

12L + 20S = 532

Which implies that 12L = 532 - 20S

Sub this expression for 12L into the first equation and we have

532 - 20S + 2S = 253 simplify

532 - 18S = 253 subtract 532 from each side

-18S = -279 divide both sides by -18

S = 279/18 = 15.5 kg

And the large box weighs

12L = 532 - 20 (15.5)

L = [ 532 - 20(15.5) ] / 12 = 18.5 kg

CPhill Aug 29, 2017