Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 8 large boxes and 4 small boxes has a total weight of 209 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 86 kilograms. How much does each type of box weigh?

Answer 1

Answer: (s for small, l for large) s=15.25 kg, l=18.5 kg.


Explanation: We need a system of equation to find the two weights of both boxes.
We can use 4s+8l=209 and 2s+3l=86.

If we multiply the second equation by -2 (for elimination), we will have -4s-6l=-172.

Combing the first equation with this new one gives us 2l=37, where dividing by 2 gives us l=18.5 kg.

We can plug 18.5 into any of the two original equations to find s.

4s+8*18.5=209
4s+148=209
4s=61
s=15.25 kg