High School

A fruit company delivers its fruit in two types of boxes: large and small.

- A delivery of five large boxes and three small boxes has a total weight of 137 kg.
- A delivery of two large boxes and six small boxes has a total weight of 128 kg.

How much does each type of box weigh?

Answer :

By setting up a system of linear equations from the deliveries data, we can solve for the weight of each box type. The large box weighs 18.25 kg and the small box weighs 15.25 kg.

To solve for the weight of each type of box, we can set up a system of linear equations based on the given deliveries. Let L represent the weight of a large box and S represent the weight of a small box. We have two deliveries that give us two equations:

  1. 5L + 3S = 137 kg (from the delivery of five large boxes and three small boxes)
  2. 2L + 6S = 128 kg (from the delivery of two large boxes and six small boxes)

By solving this system of equations, we find the weight of each box type. Let's multiply the second equation by 2.5 to match the coefficient of L's in the first equation:

  1. 5L + 3S = 137
  2. 5L + 15S = 320 (after multiplying the second equation by 2.5)

To eliminate L, we subtract the first equation from the second:

12S = 183

Dividing both sides by 12:

S = 183 / 12

S = 15.25 kg

Now we substitute S back into the first equation to solve for L:

5L + 3(15.25) = 137

5L + 45.75 = 137

5L = 137 - 45.75

5L = 91.25

L = 91.25 / 5

L = 18.25 kg

The large box weighs 18.25 kg and the small box weighs 15.25 kg.