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.