anonymous
  • anonymous
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?
Mathematics
chestercat
  • chestercat
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asnaseer
  • 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?
anonymous
  • anonymous
I guess, i'm not sure. I do not like word problems because they confuse me
asnaseer
  • asnaseer
Now, the question says it starts off as 1/6 full, so what would that be in terms of x?

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anonymous
  • anonymous
1/6x
asnaseer
  • asnaseer
correct, although we would usually write that as x/6
asnaseer
  • 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?
anonymous
  • anonymous
x/6 + 11
asnaseer
  • asnaseer
perfect! :) Finally, it says that the container is nor 2/3 full - how much would 2/3 full be in terms of x?
asnaseer
  • asnaseer
*now
anonymous
  • anonymous
2/3x
anonymous
  • anonymous
x/6 + 11 = 2/3x?
asnaseer
  • 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.
asnaseer
  • asnaseer
you're way ahead of me! :)
anonymous
  • anonymous
the container can hold 22 gallons of water. x=22
asnaseer
  • 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.
asnaseer
  • asnaseer
yes - you are right - well done! :D
anonymous
  • anonymous
Thank you so much for the step by step help. It helps me understand the problem.!
asnaseer
  • asnaseer
yw :)

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