Question

When a jug is half- filled with marbles, it weighs 2.6 kg. The jug weighs 4 kg when it is full. Find the weight of the empty jug.

Answer 1

The jug weights empty 1.2 kg.

Explanation:

In this case we can define two equations based on the description to find the weight of the empty jug, this is:

Eq. 1:
`Jug+(1)/(2) Marbles=2.6`

Eq. 2:
`Jug+Marbles=4`

Now putting the Eq. 2 in the Eq. 1 we have:

`Jug+(1)/(2) (4-Jug)=2.6`

Clearing Jug:

`(1)/(2)Jug=2.6-2`

`Jug=0.6*2`

`Jug=1.2`

The jug weights empty 1.2 kg.

Answer 2

the difference between a full jug and a jug that is half full will give us the weight of the marbles only in a half full jug:
4 - 2.6 = 1.4 kg

In a half full jug that weighs 2.6 kg, the weight of the marbles is 1.4 kg
the weight of the jug = 2.6 - 1.4 = 1.2 kg