Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes has a total weight of 133 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 69 kilograms. How much does each type of box weigh?​

Answer 1

The large box contains 18.5 kg of fruit.

The small box contains 6.75 kg of fruit.

Explanation:

We know that 3L + 2S = 69 and 5L + 6S = 133.

In order to solve for one variable, we can multiply the first equation by 3 so we can eliminate S.

The new equations are 9L + 6S = 207 and 5L + 6S = 133.

Now, we can subtract the equations from each other to solve for one variable, L.

We now get 4L = 74, and when we divide 4 from both sides, we get L = 18.5. This means that a large box has 18.5 kg of fruit.

Now that we know what the large box contains, we can plug the answer into one of the original equations to solve for S.

We now get 3(18.5) + 2S = 69, which we can solve by distributing to get 55.5 + 2S = 69, subtracting 55.5 from both sides to get 2S = 13.5, and then dividing 2 from both sides to get S = 6.75.

We now know both boxes, with the large containing 18.5 kg and the small containing 6.75 kg.