Question

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

Answer 1

Large box:
`18.5\ kilograms`

Small box:
`15.25\ kilograms`

Explanation:

Let be "l" the weight in kilograms of a large box and "s" the weight in kilograms of a smalll box.

Set up a system of equations:

`\left \{ {{3l+2s=86} \atop {8l+4s=209}} \right.`

In order to solve the system of equations, you can apply the Elimination Method. Multiply the first equation by -2, add the equations and then solve for "l":

`\left \{ {{-6l-4s=-172} \atop {8l+4s=209}} \right.\\......................\\2l=37\\\\l=(37)/(2)\\\\l=18.5`

Finally, susbstitute the value of "l" into any original equation and solve for "s":

`3(18.5)+2s=86\\\\2s=86-55.5\\\\s=(30.5)/(2)\\\\s=15.25`