Water Bottle

Let weight of bottle be x and weight of half the amount of water in bottle initially be y.

x+2y=15

x+y=10 or 2x+2y=20

subtracting first equation from second, we get x=5.

$B=mass~of~bottle$

$W=mass~of~water$

$B+W=15$ $\implies$ $W=15-B$ $\color{#D61F06}(1)$

$B+\dfrac{1}{2}W=10$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$

$B+\dfrac{1}{2}(15-B)=10$ $\implies$ $B+\dfrac{15}{2}-\dfrac{B}{2}=10$ $\implies$ $\dfrac{1}{2}B=10-\dfrac{15}{2}$ $\implies$ $\color{#3D99F6}\boxed{B=5}$

x means bottle weight,y means water weight. x+y=15.....(1) x+1/2 (y)=10......(2) from( 2), 2x+y=20......(3) then, (3)-(1) x=5

5kg.. wth, how huge this glass bottle.. how can you brought such of this thing? anyway this is a barrel not a bottle.. or maybe a bottle with lid made from a barble

Let x represent the mass of the bottle (in kg). Let y represent the mass of the water (in kg).

1. x+y = 15
2. x+0.5y = 10

Using the method of elimination... x+y = 15 (subtraction) x+0.5y = 10

---

                                 0.5y = 5

Since 0.5y = 5, multiplying both sides by 2 shows that y = 10

Now we substitute this value into the first equation: x+(10) = 15 x = 5

Therefore, the mass of the bottle is 5 kg.

let total weight of glass be x kg

(15-x)= 2(10-x) 15-x = 20-2x x=5

It is a simple system of equations / matrix: It can be solved by hand, a calculator, or a program in C.

| 1 1 15 |

| .5 1 10 |

The first column represents weight of the water while the second column represenrs the weight of the glass. :)

Simple ..mass of bottle with fully filled water is 15kg and half filled is 10 kg so the difference is 5kg ..the mass of bottle is same so the difference 5 kg is mass of water increase that is the mass of water that occupies the remaining half and is equal to the present half ..from the given problen the mass of half filled bottle is 10kg so when we substitute mass of water we get mass of bottle is 5kg.

mass(B)+mass(w)=15................(1) mass(B)+0.5*mass(w)=10..........(2)

if we do equation (1) - equation (2) >>> then we will find>> mass (w)=10 putting this value of mass(w) in equation(1) or equation (2)>>>> then we can find >>> mass(B)=5