Question

A fruit company delivers its fruit in two types of boxes : large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 190 kilograms. A delivery of 2 large boxes and 3 small boxes has a total of 84 kilograms. How much does each type of boxes weigh ?

Answer 1

We have this system

6L + 5S = 190 (1)

2L + 3S = 84 multiply through by -3 ⇒ -6L - 9S = -252 (2)

Add (1) and (2) and we get that

-4S = -62

S = -62 / -4 = 15.5 kilos for a small box

And

2L + 3S = 84

2L + 3 (15.5) = 84

2L = 46.5 = 84

2L = 84 - 46.5

2L = 37.5

L = 37.5 /2 = 18.75 kilos for a large box

Answer 2

4 large and 8 small weigh 113kg
so
2 large and 4 small weigh 56.5 kg
but
2 large and 3 small weigh 50 kg
so taking the difference
1 small weighs 56.5 - 50 = 6.5 kg.

Substitute :
2 large and 3 small weight 50 kg
2 large weigh 50 - 3*6.5 = 50 - 19.5 = 30.5 kg
1 large weighs 15.25 kg