Question

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.

Answer 1

@Michele_Laino

Answer 2

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

Answer 3

correct! @i_dont_know_

Answer 4

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

Answer 5

(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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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=...?

Answer 10

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

Answer 11

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

Answer 12

ok but whats this?
q=r⋅b=1/5(2/3)b⋅b=

Answer 13

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

Answer 14

i dont know the answer to that :(

Answer 15

ok! then look at the proportion of @i_dont_know_ above

Answer 16

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

Answer 17

im so confused :(

Answer 18

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

Answer 19

can you just please give me the answer :)

Answer 20

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

Answer 21

3/10

Answer 22

@Michele_Laino