A container is $\displaystyle \frac {1}{8}$ full of liquid. After 10 cups of liquid are added, the container is $\displaystyle \frac {3}{4}$ full. What is the volume of the container in cups?

Can't seem to figure out why it's 16.

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- Apr 24th 2010, 05:09 PMmjoshuafractions problem
A container is $\displaystyle \frac {1}{8}$ full of liquid. After 10 cups of liquid are added, the container is $\displaystyle \frac {3}{4}$ full. What is the volume of the container in cups?

Can't seem to figure out why it's 16. - Apr 24th 2010, 06:35 PMmaddas
Let $\displaystyle V$ be the volume of the container in cups. Then what you have asserted means that $\displaystyle \frac18V + 10 = \frac34 V$, so, rearranging, $\displaystyle V = 10 / (\frac34-\frac18) = 16$.

- Apr 24th 2010, 07:13 PMDeanSchlarbaumPossible Solution -- Think Decimals
The container begins 1/8 or 12.5% full. Then after 10 cups added, container is 75%. 75% (.75) minus 12.5% (.125) = 62.5%. So, the 10 cups that were added filled the container 62.5% (.625). This means that each cup filled the container 6.25% (.0625). So, the 1/8 full, which accounted for 12.5% (.125) amounted to 2 cups already in container. Now, 10 cups + 2 cups = 12 cups = the container 75% full. So, to find the volume of the container you would divide 12 by .75. Do this and see what result you get. And, does the reasoning behind the solution make sense to you?