Question

Nancy left a bin outside in her garden to collect rainwater. She notices that 1/2 gallon of water fills 2/3 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

Answer:

$\frac{3}{4}$ gallon.

Step-by-step explanation:

Let x represent the amount of water needed to fill the bin.

We have been given that Nancy left a bin outside in her garden to collect rainwater. She notices that 1/2 gallon of water fills 2/3 of the bin.

$\frac{1}{2}\div \frac{2}{3}=x$

Convert to multiplication problem:

$\frac{1}{2}\times \frac{3}{2}=x$  

$\frac{3}{4}=x$

Therefore, $\frac{3}{4}$ gallon can fill the entire bin.

Answer 2

1. You have that 1/2 gallon of water fills 2/3 of the bin.

2. Therefore, you must use proportions.
 
 3. Let's call "x" to the amount of water that will fill the entire bin. Then, you have:
 
 (1/2)/(2/3)=(x/3/3)
 1/2)/(2/3)=(x/1)
 
 4. Now, you must clear "x", as below:
 
 (1x3/2x2)=(x/1)
 3/4=x
 x=3/4
 

  The amount of water that will fill the entire bin is 3/4 gallons.