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rosimary 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? one year ago one year ago

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1. asnaseer

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?

2. rosimary

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

3. asnaseer

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

4. rosimary

1/6x

5. asnaseer

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

6. asnaseer

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?

7. rosimary

x/6 + 11

8. asnaseer

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

9. asnaseer

*now

10. rosimary

2/3x

11. rosimary

x/6 + 11 = 2/3x?

12. asnaseer

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.

13. asnaseer

you're way ahead of me! :)

14. rosimary

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

15. asnaseer

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.

16. asnaseer

yes - you are right - well done! :D

17. rosimary

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

18. asnaseer

yw :)