# 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?

**Answer:**

**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

Adding both equation, we get

-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**

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