Question

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

3 large boxes and
5 small boxes has a total weight of
116 kilograms. A delivery of
9 large boxes and
7 small boxes has a total weight of
238 kilograms. How much does each type of box weigh?

Answer 1

Small box weighs 13.75 kg & large box weighs 15.75 kg

Explanation:

We can write 2 simultaneous equation and solve for weight of each box.

Let weight of large box be l and small box be s.

"3 large boxes and 5 small boxes has a total weight of 116 kilograms":

`3l+5s=116`

and

"9 large boxes and 7 small boxes has a total weight of 238 kilograms":

`9l+7s=238`

Now we can solve for l in the 1st equation and put it into 2nd equation and get s:

`3l+5s=116\\3l=116-5s\\l=(116-5s)/(3)`

now,

`9l+7s=238\\9((116-5s)/(3))+7s=238\\3(116-5s)+7s=238\\348-15s+7s=238\\348-238=15s-7s\\110=8s\\s=(110)/(8)=13.75`

now we plug in 13.75 into s into equation of l to find s:

`l=(116-5s)/(3)\\l=(116-5(13.75))/(3)\\l=15.75`