Question

Word Problem: The container that holds the water for the football team is 1/6 full. After pouring in 11 gallons of water, it is 2/3 full. How many gallons can the container hold?

Answer 1

Start by letting x represent the capacity of the container.
Now, the question says it starts off as 1/6 full, so what would that be in terms of x?

Answer 2

I guess, i'm not sure. I do not like word problems because they confuse me

Answer 3

Now, the question says it starts off as 1/6 full, so what would that be in terms of x?

Answer 4

1/6x

Answer 5

correct, although we would usually write that as x/6

Answer 6

Next, it says that 11 gallons was poured in. So if the container currently contains x/6 gallons, and we pour in 11 more gallons, then how many gallons do we have now?

Answer 7

x/6 + 11

Answer 8

perfect! :)

Finally, it says that the container is nor 2/3 full - how much would 2/3 full be in terms of x?

Answer 9

*now

Answer 10

2/3x

Answer 11

x/6 + 11 = 2/3x?

Answer 12

great!

so - summarising - we know that at the end of all this, the container contains x/6 + 11 gallons, and we also know that it is 2/3 full so it contains 2x/3 gallons.

So all we need to do now is to equate the two expressions to get:\[\frac{x}{6}+11=\frac{2x}{3}\]and solve for x.

Answer 13

you're way ahead of me! :)

Answer 14

the container can hold 22 gallons of water. x=22

Answer 15

The easiest way to solve fractional expressions is to try and first get rid of the fractions. So, notice that if you multiply both sides of this equation by 6 then you can get rid of the fractions.

Answer 16

yes - you are right - well done! :D

Answer 17

Thank you so much for the step by step help. It helps me understand the problem.!

Answer 18

yw :)