## anonymous one year ago 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.

1. anonymous

@phi @mathmath333

2. anonymous

@imqwerty @dan915 @Elsa213 @JayJayTheWereWolfGal1

3. phi

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

4. anonymous

Yes it does

5. 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 $\frac{ \frac{1}{2}}{\frac{2}{3}} = \frac{x}{1}$

6. phi

or you could say 2/3 of a full bin is 1/2 gallon 2/3 x = 1/2 $\frac{2}{3} x= \frac{1}{2}$

7. anonymous

OK the second one makes more sense

8. phi

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

9. anonymous

Multiply 12?

10. anonymous

@phi

11. phi

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