anonymous
  • anonymous
Jason left a bin outside in his garden to collect rainwater. He notices that 1 over 5 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
katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
2/3x = 1/5 with x representing 1 entire bin
Michele_Laino
  • Michele_Laino
correct! @i_dont_know_

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anonymous
  • anonymous
@Michele_Laino whats the complete answer :) please include all the work !
anonymous
  • anonymous
(1/5) / (2/3) = x/1 --- (1/5 water to 2/3 bin = x water to 1 bin) now we cross multiply 2/3x = 1/5 x = (1/5) / (2/3) x = 1/5 * 3/2 x = 3/10 check 1/5 = 2/3 of 3/10 1/5 = 2/3 * 3/10 1/5 = 6/30 1/5 = 1/5
Michele_Laino
  • Michele_Laino
more explanation: the filling rate is: \[r = \frac{{1/5}}{{\left( {2/3} \right)b}}\] now, in order to get the right equation for amount q of water, we have to multiply that rate by the area of the bin \( b \) so we get: \[q = r \cdot b = \frac{{1/5}}{{\left( {2/3} \right)b}} \cdot b = ...?\]
texaschic101
  • texaschic101
I would normally set it up as a proportion...like i_don't_know_ did...
Michele_Laino
  • Michele_Laino
oops... not area of bin, the volume of bin
anonymous
  • anonymous
so is this the full answer? the filling rate is: r=1/5(2/3)b now, in order to get the right equation for amount q of water, we have to multiply that rate by the area of the bin b so we get: q=r⋅b=1/5(2/3)b⋅b=...?
anonymous
  • anonymous
i dont know this :( q=r⋅b=1/5(2/3)b⋅b=
Michele_Laino
  • Michele_Laino
another way is to write a proportion, please look at the reply of @i_dont_know_
anonymous
  • anonymous
ok but whats this? q=r⋅b=1/5(2/3)b⋅b=
Michele_Laino
  • Michele_Laino
I meant: b stands for bin so 1/5 of gallon of water is needed to fill 2/3 of bin, then the filling rate, is: \[r = \frac{{1/5}}{{\left( {2/3} \right)b}}\] now, in order to get the requested amount q of water, we have to multiply r by b so we can write: \[q = r \cdot b = \frac{{1/5}}{{\left( {2/3} \right)b}} \cdot b = ...?\]
anonymous
  • anonymous
i dont know the answer to that :(
Michele_Laino
  • Michele_Laino
ok! then look at the proportion of @i_dont_know_ above
Michele_Laino
  • Michele_Laino
if q is the requested amount of water, then we can write: \[q:1 = 1/5:2/3\]
anonymous
  • anonymous
im so confused :(
Michele_Laino
  • Michele_Laino
and, if I apply the fundamental property of proportion, I get: \[q = \frac{{1/5}}{{2/3}} = ...?\]
anonymous
  • anonymous
can you just please give me the answer :)
Michele_Laino
  • Michele_Laino
hint: \[q = \frac{{1/5}}{{2/3}} = \frac{1}{5} \cdot \frac{3}{2} = ...?\]
anonymous
  • anonymous
3/10
anonymous
  • anonymous

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