weighing?

Oct 2008
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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?
 

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MHF Helper
Aug 2008
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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.
 
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Soroban

MHF Hall of Honor
May 2006
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Lexington, MA (USA)
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]: . \(\displaystyle J + 8\tfrac{1}{2} \:=\:10 \quad\Rightarrow\quad\boxed{ J \:=\:1\tfrac{1}{2}\text{ pounds}}\)
 
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