Word Problem (basic algebra, yet I'm stuck)

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ellymane

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May 27, 2007
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Question: If a jug is still a 1/3 full (of juice) and a person spilled 550 milliliters of the juice, how many millilters does the jug hold?

So I was able to figure that 2/3 of the jug is 550 milliters by subtracting 1 from 1/3....but now, how do I figure out how many milliters are in a 1/3 of the jug?

I'm having difficulty picturing this problem.
 
Hello, ellymane!

If a jug is still a 1/3 full (of juice) after a person spilled 550 milliliters of the juice,
how many millilters does the jug hold?

So I was able to figure that 2/3 of the jug is 550 milliters by subtracting 1 from 1/3.
. . Good!

But now, how do I figure out how many milliters are in a 1/3 of the jug?
I'm having difficulty picturing this problem.
Click to expand...

That's the key word: picture!
Code: 
      *-----------*  -
      |           |  :
      |           |  :
      |           |  :
      +   550ml   + 2/3
      |           |  :
      |           |  :
      |           |  :
      + - - - - - +  -
      |           |  :
      |     ?     | 1/3
      |           |  :
      *-----------*  -

If two-third of the jug is 550 ml,
. . then one-third of the jug must be: \(\displaystyle \,550\,\div\,2\:=\:275\) ml.

Therefore, the whole jug contains . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

You're probably expected to use Algebra, right?

Let \(\displaystyle x\) = capacity of the jug (in milliliters).

We know that: \(\displaystyle \:\underbrace{\text{two-thirds}}\:\underbrace{\text{of}}\;\underbrace{\text{the jug}}\:\underbrace{\text{is}}\;\underbrace{550}\text{ ml}\)
. . . . . . . . . . . . . . . .\(\displaystyle \downarrow\;\;\;\;\;\,\downarrow\;\;\;\;\downarrow\;\;\;\,\downarrow\;\:\downarrow\)
. . . . . . . . . . . . . . . .\(\displaystyle \frac{2}{3}\;\;\;\;\;\;\times \;\;\;\;\;x\;\;\:\:=\;550\)


And there is our equation! . . . \(\displaystyle \;\frac{2}{3}x \:=\:550\)

Multiply both sides by \(\displaystyle \frac{3}{2}:\;\;\frac{3}{2}\left(\frac{2}{3}x\right) \:=\:\frac{3}{2}(550)\;\;\Rightarrow\;\;\L\fbox{x\:=\:825}\)

 
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