A bathtub is filled with 100 gallons of water. A cup of milk is then poured in and mixed thoroughly with the 100 gallons of water. A cup of liquid is then taken out and placed in a bowl. What fraction of the liquid in the bowl is milk? What is the ratio of milk to water?
16 cups = 1 gallon
100 gallons = 1,600 cups
1 cup milk to 1,600 cups water
1/1600
To solve this problem, we need to determine the fraction of milk in the bowl and the ratio of milk to water.
First, let's determine the amount of milk in the bowl. We know that a cup of milk was added to the 100 gallons of water in the bathtub. A standard cup is equal to 8 fluid ounces or 1/16 of a gallon. So, the amount of milk added to the bathtub is 1/16 of a gallon.
Next, a cup of liquid is taken out of the bathtub and placed in the bowl. We assume that this cup has the same capacity as the cup of milk previously added, which is 1/16 of a gallon.
Since the cup of milk is equal to the cup of the liquid taken out, the fraction of milk in the bowl is 1/16.
To determine the ratio of milk to water, we need to find the amount of milk and water in the bathtub. The amount of water in the bathtub is 100 gallons, and the amount of milk added is 1/16 of a gallon. So the ratio of milk to water is 1/16 : 100, or simply 1:1600.
Therefore, the fraction of the liquid in the bowl that is milk is 1/16, and the ratio of milk to water is 1:1600.