1. weighing?

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?

2. Originally Posted by 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?
Let j = weight of jar
Let w = weight of water when jar is full

So we get the following system of equations

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

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

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

Subtract the first equation from the second, you get

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

$j = 1.5$.

So the weight of the jar is 1.5 pounds.

3. 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 $J$ = weight of the jar.
Let $W$ = weight of the water.

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

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

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