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.

Question

anonymous · Answer

@phi 
@mathmath333

anonymous · Answer

@imqwerty  @dan915  @Elsa213 @JayJayTheWereWolfGal1

phi · Answer

does that say 1/2 gallons fills 2/3 of the barrel?

anonymous · Answer

Yes it does

phi · Answer

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 · Answer

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 · Answer

OK the second one makes more sense

phi · Answer

to solve the second one, multiply both sides by 3/2  
and simplify

anonymous · Answer

Multiply 12?

anonymous · Answer

@phi

phi · Answer

you should get
$$x= \frac{3}{2}\cdot \frac{1}{2} = \frac{3}{4} $$

3/4 of a gallon will fill the bin.