Question

The container that holds the water for the football team is 1/4 full. After pouring in 6 gallons of water, it is 5/8 full. How many gallons can the container hold?

Answer 1

Hint 5/8-1/4=3/8

Answer 2

First change the fractrion 1/4 to 2/8. This is to make it easier to deal with the fractions when the denominators are the same. So at first, the container was 2/8 full. (We multipled the top and bottom by 2)

Next, when 6 gallons of what is added, it's 5/8 full. This means that (2/8) which is the inital volume, plus x (x is the amount of water that was added) is 5/8. We now solve for x. (x is 6 gallons but solving for x will tell us exactly what fraction of the container is 6 gallons.)

\[\frac{ 2 }{ 8 } + x = \frac{ 5 }{8 }\]
\[x = \frac{ 5 }{ 8 }-\frac{ 2 }{ 8 }\]
\[x=\frac{ 3 }{ 8 }\]

Ok so now we know that the 6 gallons of water is 3/8 the volume of the entire container.
Now we just need to find the volume the whole container and how many gallons would fill the whole container. To do this, we know that 3/8 of the volume is 6 gallons, so we can divide 8/8 (8/8 refers to the entire of the volume of the container) by 3/8 to see how many times it would fit to fill the entire container. Thise will also tell us how many times 6 gallons will go in to the container to completely fill it. This is how it looks:

\[\frac{ 8 }{ 8 } \div \frac{ 3 }{ 8 } = \frac{ 8 }{ 8 } * \frac{ 8 }{ 3 }=\frac{ 64 }{ 24 }=\frac{ 8 }{ 3 }\]
So now we know that 3/8 of the volume of the container can fill the whole volume 8/3 times. This also means that the volume of the container is 6 gallons of water times 8/3, which means that 6 gallons of water will fit 8/3 times to fill the volume of the entire container. This is how this would look:

\[\frac{ 6 }{ 1 }*\frac{ 8 }{ 3 }=\frac{ 48 }{ 3 }\]
\[\frac{ 48 }{ 3 }=16\]
\[\therefore \] The container can hold 16 gallons of water.

Answer 3

Let x be the container's capacity. Solve the following for x:\[\frac{1}{4} x+ 6 =\frac{5}{8} x\]\[x=16 \text{ gallons}\]