Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms. A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms. How much does each type of box weigh?

Answer 1

Weight of Large Box = 18.5 kg

Weight of Large Box = 13.25 kg

Explanation:

Given:

There are two types of boxes i.e. Large and Small

Let the weight of Large boxes = L kg

Let the weight of Small boxes = S kg

As per given statement:

• A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms.

Writing equation for above:

`8L + 4S = 201` ....... (1)

• A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms.

Writing equation for above:

`3L + 2S = 82 ....... (2)`

Now, by solving the equations (1) and (2), we can get the values of L and S.

Multiplying equation (2) with 2 and subtracting from equation (1):

`8L + 4S = 201`

-

`2 * (3L + 2S) = 82 * 2`

`8L + 4S = 201`

-

`6L + 4S = 164`

--------------------

`2L = 37`

L = 18.5 Kg

Putting value of L in equation (1):

`8 * 18.5 + 4S = 201\\\Rightarrow 148 + 4S = 201\\\Rightarrow 4S = 201 - 148\\\Rightarrow 4S = 53\\\Rightarrow S = 13.25\ kg`

So, the answer is:

Weight of Large Box = 18.5 kg

Weight of Large Box = 13.25 kg