Question

A bottle filled with water weighs 1kg . The same bottle filled 1/3 with water weighs 640g. What is the weight of the bottle? (1kg=1000g)

The bottle alone weighs x grams and the water in the full bottle weighs y grams.

Write two equations.

Answer 1

This problem is easily solved without system of equations.
Bottle + water = 1000 g
bottle + 1/3 water = 640 g
Subtract to get 2/3 water = 360 g
so water weighs 360/(2/3)=540 g
bottle weighs 1000-540=460 g

Using equations
B=weight of bottle
W=weight of water
the two equations are
B+W=1000
B+W/3=640
For the purpose of the question, use x=bottle, y=water.
However, it is always a better idea to use letters that tell you something than x, y.

Answer 2

weight of the bottle alone = 460 gm

Explanation:

Let the weight of bottle without water = x gm

and let the weight of the bottle with full of water = y gm

Now, it has been given that bottle filled with water weighs 1 kg or 1000 gm.

Thus, the equation is

`x+y=1000...(i)`

Now, the same bottle filled 1/3 with water weighs 640 gm. Hence, the second equation is

`x+(y)/(3)=640...(ii)`

Subtract (i) and (ii) and solve the equation for y

`y-(y)/(3)=360\\\\(2y)/(3)=360\\\\2y=1080\\\\y=540`

Substituting this value in (i)

x + 540 = 1000

x = 1000 - 540

x = 460

Hence, the weight of the bottle alone = 460 gm