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?

Printable View

- Oct 14th 2008, 07:52 PMfecoupefeweighing?
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?

- Oct 14th 2008, 07:58 PMProve It
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. - Oct 14th 2008, 08:04 PMSoroban
Hello, fecoupefe!

Quote:

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