# weighing?

#### fecoupefe

A jar filled with water weighs 10 pounds. When one-half of the water is poured out, the jar and remaining water weigh 5 3/4 pounds. How much does the jar weigh?

#### Prove It

MHF Helper
A jar filled with water weighs 10 pounds. When one-half of the water is poured out, the jar and remaining water weigh 5 3/4 pounds. How much does the jar weigh?
Let j = weight of jar
Let w = weight of water when jar is full

So we get the following system of equations

$$\displaystyle j + w = 10$$
$$\displaystyle j + \frac{1}{2}w = 5.75$$.

Multiply the second equation by 2, and the system of equations becomes

$$\displaystyle j + w = 10$$
$$\displaystyle 2j + w = 11.5$$

Subtract the first equation from the second, you get

$$\displaystyle 2j + w - (j + w) = 11.5 - 10$$

$$\displaystyle j = 1.5$$.

So the weight of the jar is 1.5 pounds.

fecoupefe

#### Soroban

MHF Hall of Honor
Hello, fecoupefe!

A jar filled with water weighs 10 pounds.
When one-half of the water is poured out, the jar and remaining water weigh 5¾ pounds.
How much does the jar weigh?

Let $$\displaystyle J$$ = weight of the jar.
Let $$\displaystyle W$$ = weight of the water.

We have: . $$\displaystyle \begin{array}{cccc}J + W &=& 10 & {\color{blue}[1]} \\ J + \frac{1}{2}W &=& 5\frac{3}{4} & {\color{blue}[2]} \end{array}$$

Subtract $$\displaystyle {\color{blue}[1] - [2]}$$: . $$\displaystyle \tfrac{1}{2}W \:=\:4\tfrac{1}{4} \quad\Rightarrow\quad W \:=\:8\tfrac{1}{2}$$

Substitute into [1]: . $$\displaystyle J + 8\tfrac{1}{2} \:=\:10 \quad\Rightarrow\quad\boxed{ J \:=\:1\tfrac{1}{2}\text{ pounds}}$$

fecoupefe