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anonymous

  • one year ago

The container that holds the water for the football team is 1/3 full. After pouring out 6 gallons of water, it is 1/9 full. How many gallons can the container hold?

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  1. phi
    • one year ago
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    think like this: let "x" be the number of gallons when full. How many gallons in the container when 1/3 full? you write x/3 (that means we divide the number of gallons by 3)

  2. anonymous
    • one year ago
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    alright..

  3. phi
    • one year ago
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    now pour out 6 that is like "subtracting" x/3 - 6

  4. phi
    • one year ago
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    what we now have is it is 1/9 full. any idea how to write that using x?

  5. anonymous
    • one year ago
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    =x/9?

  6. phi
    • one year ago
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    yes. we have \[ \frac{x}{3} - 6 = \frac{x}{9} \] now we switch from "what is going on mode" to "algebra mode" to solve I would multiply both sides (and all terms) by 9 (this will get rid of the fractions)

  7. anonymous
    • one year ago
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    if i do x/3-6=x/9 then x would equal 27

  8. phi
    • one year ago
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    the point of doing this is not the answer, it is how you get the answer.

  9. anonymous
    • one year ago
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    okay so I would multiply each side by 9 and get rid of things then it would be 3 multiplied by 9

  10. phi
    • one year ago
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    like this \[ 9 \cdot \frac{x}{3} - 9 \cdot 6 = 9 \frac{x}{9} \]

  11. anonymous
    • one year ago
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    so then because it equals 27 (3 times 9 does) would i subtract 6 and have the answer of 21?

  12. phi
    • one year ago
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    the first term \[ 9\cdot \frac{x}{3} \] or \[ \frac{9 \cdot x}{3} \] you can divide 3 into 9

  13. phi
    • one year ago
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    or, 9/3 is ?

  14. anonymous
    • one year ago
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    wouldnt it be 9 times x/3

  15. phi
    • one year ago
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    yes 9 times x/3 which you write as \[ 9 \cdot \frac{x}{3} \] or \[ \frac{9\cdot x}{3} \] or \[ \frac{9}{3} \cdot x \] all different ways of writing the same thing. but the important part is it means you can divide 3 into 9

  16. phi
    • one year ago
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    Is this confusing? If it is , it is worth figuring it out, because algebra uses this a *lot*

  17. anonymous
    • one year ago
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    yes im super confused

  18. phi
    • one year ago
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    If you have time, you can learn the idea You know how to figure out \[ \frac{4}{2} \] = 2 right?

  19. phi
    • one year ago
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    4 is the same as 2*2 so we could write the problem as \[ \frac{2\cdot 2}{2} \] and we know the answer is still 2

  20. phi
    • one year ago
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    or , another example, \[ \frac{30}{5} = \frac{2\cdot 3\cdot 5}{5} \] if you divide 5/5 you get \[ \frac{2\cdot 3\cdot \cancel{5}}{\cancel{5}} = \frac{2\cdot 3}{1}= 6\]

  21. phi
    • one year ago
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    and you know 30/5 = 6 we got the correct answer. we use that same trick with \[ \frac{9 x}{3} = \frac{3 \cdot 3 \cdot x}{3} \] or, using the trick \[ \frac{\cancel{3} \cdot 3 \cdot x}{\cancel{3}} = \frac{3x}{1} = 3x\]

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