## anonymous one year ago 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.

1. anonymous

@Michele_Laino

2. anonymous

2/3x = 1/5 with x representing 1 entire bin

3. Michele_Laino

correct! @i_dont_know_

4. anonymous

@Michele_Laino whats the complete answer :) please include all the work !

5. 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

6. 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: $q = r \cdot b = \frac{{1/5}}{{\left( {2/3} \right)b}} \cdot b = ...?$

7. texaschic101

I would normally set it up as a proportion...like i_don't_know_ did...

8. Michele_Laino

oops... not area of bin, the volume of bin

9. 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=...?

10. anonymous

i dont know this :( q=r⋅b=1/5(2/3)b⋅b=

11. Michele_Laino

another way is to write a proportion, please look at the reply of @i_dont_know_

12. anonymous

ok but whats this? q=r⋅b=1/5(2/3)b⋅b=

13. 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: $q = r \cdot b = \frac{{1/5}}{{\left( {2/3} \right)b}} \cdot b = ...?$

14. anonymous

i dont know the answer to that :(

15. Michele_Laino

ok! then look at the proportion of @i_dont_know_ above

16. Michele_Laino

if q is the requested amount of water, then we can write: $q:1 = 1/5:2/3$

17. anonymous

im so confused :(

18. Michele_Laino

and, if I apply the fundamental property of proportion, I get: $q = \frac{{1/5}}{{2/3}} = ...?$

19. anonymous

20. Michele_Laino

hint: $q = \frac{{1/5}}{{2/3}} = \frac{1}{5} \cdot \frac{3}{2} = ...?$

21. anonymous

3/10

22. anonymous

@Michele_Laino