Nancy left a bin outside in her garden to collect rainwater. She noticed that 1/2 gallon of water fills 2/3 of the bin right and solve an equation to find the amount of water that will fill the entire bin.
Let's assume that the amount of water that fills the entire bin is x gallons.
According to the given information, 1/2 gallon of water fills 2/3 of the bin. So, the ratio of the amount filled to the capacity is (1/2) / (2/3) = 1/2 * 3/2 = 3/4.
Therefore, we can set up the equation: (3/4)x = 1.
To solve for x, we multiply both sides of the equation by (4/3):
x = 4/3.
Hence, the amount of water that will fill the entire bin is 4/3 gallons.