A fruit company delivers its fruit in two types of boxes: large and small. Delivery of 4 large boxes and 8 small boxes has a total weight of 105 kilograms. Delivery of 2 large boxes and 3 small boxes has a total weight of 46 kilograms. How much does each type of box weigh?

x = 13.25 kg

y = 6.5 kg

Step-by-step explanation:

Let

Large box = x

Small box = y

4x + 8y = 105 (1)

2x + 3y = 46 (2)

(Multiply (2) by 2 to eliminate x

2x + 3y = 46 (2) ×2

4x + 6y = 92 (3)

4x + 8y = 105 (1)

Subtract (3) from (1)

8y - 6y = 105 - 92

2y = 13

y = 13/2

y = 6.5kg

Substitute y = 6.5 into (2)

2x + 3y = 46 (2)

2x + 3(6.5) = 46

2x + 19.5 = 46

2x = 46 - 19.5

2x = 26.5

x = 26.5/2

x = 13.25 kg