A fruit 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 123 kilograms. A delivery of 12 large boxes and 2 small boxes and 2 small boxes has a total weight of 249 kilograms. how much does each type of box weigh?

The weight of a small box  = 13.5 kg

The weight of 1 large box = 18.5 kg

Step-by-step explanation:

Let us assume the weight of a small box = m kg

And the weight of 1 large box  = n kg

Now, the weight of 5 small box = 5 x (weight of 1 small box) =  5 m

Also, the weight of 3 large box = 3 x (weight of 1 large box) =  3 n

Here,   3 large boxes +  5 small boxes =  of 123 kilograms

5  m + 3 n = 123   .... (1)

Again, the weight of 2 small box = 2 x (weight of 1 small box) =  2 m

Also, the weight of 12 large box = 12 x (weight of 1 large box) =  12 n

Here,   12 large boxes +  2 small boxes =  249 kilograms

2 m+ 12 n = 249   .... (2)

Now, solving both the given equations by ELIMINATION, we get:

5  m + 3 n = 123     x (2)

2 m+ 12 n = 249     x (-5)

we get the new set of equitation as:

10 m + 6 n = 246

- 10 m - 60 n =  -1245

-54 n = 999

or, n = 18.5

Now, 5  m + 3 n = 123

So, 5 m = 123  -3 (18.5)  = 123 - 55.5 =  67.5

⇒  m = 13.5

Hence,  the weight of a small box = m kg = 13.5 kg

And the weight of 1 large box = n kg  = 18.5 kg