Question

a fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 73 kg. A delivery of 8 large boxes and 4 small boxes has a total weight of 177 kg. how much does each type of box weigh?

Answer 1

Explanation:

3L + 2S = 73 .....multiply by -2

8L + 4S = 177

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-6L - 4S = - 146 (result of multiplying by -2)

8L + 4S = 177

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2L = 31

L = 31/2

L = 15.5 <=== large boxes weigh 15.5 kg (or 15 1/2 kg)

3L + 2S = 73

3(15.5) + 2S = 73

46.5 + 2S = 73

2S = 73 - 46.5

2S = 26.5

S = 26.5 / 2

S = 13.25 <=== small boxes weigh 13.25 kg (or 13 1/4 kg)

Answer 2

x = the wight of the large box

y = the weight of the small box

A delivery of 3 large boxes and 2 small boxes has a total weight of 73 kilograms.

3x + 2y = 73

A delivery of 8 large boxes and 4 small boxes has a total weight of 177 kilograms.

8x + 4y = 177

by solving the system of equations

3x + 2y = 73

8x + 4y = 177

we find

x = 15.5 kg

y = 13.25 kg

the large box weights 15.5 kg.

the small box weights 13.25 kg.