anonymous
  • anonymous
Nancy left a bin outside in her garden to collect rainwater. She notices that 1 over 2 gallon of water fills 2 over 3 of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.
Mathematics
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anonymous
  • anonymous
Nancy left a bin outside in her garden to collect rainwater. She notices that 1 over 2 gallon of water fills 2 over 3 of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
phi
  • phi
does that say 1/2 gallons fills 2/3 of the barrel?

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anonymous
  • anonymous
Yes it does
phi
  • phi
you could use ratios: 1/2 is to 2/3 as x is to 1 which says 1/2 gallon is to 2/3 of a bin as an unknown number of gallons (call it x) is to 1 (full) bin \[ \frac{ \frac{1}{2}}{\frac{2}{3}} = \frac{x}{1} \]
phi
  • phi
or you could say 2/3 of a full bin is 1/2 gallon 2/3 x = 1/2 \[ \frac{2}{3} x= \frac{1}{2} \]
anonymous
  • anonymous
OK the second one makes more sense
phi
  • phi
to solve the second one, multiply both sides by 3/2 and simplify
anonymous
  • anonymous
Multiply 12?
anonymous
  • anonymous
phi
  • phi
you should get \[x= \frac{3}{2}\cdot \frac{1}{2} = \frac{3}{4} \] 3/4 of a gallon will fill the bin.

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