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