To make punch for her upcoming party, Mary used a recipe that calls for 1/2 cup of fruit juice per serving. If she has e gallons of fruit juice, what is the greatest number of servings of punch she can make? (note: 1 gallon=16 cups)
To find the greatest number of servings of punch Mary can make, we need to determine how many servings can be made with the given amount of fruit juice.
First, we need to convert the measurement of the fruit juice from gallons to cups. Since 1 gallon is equal to 16 cups, we can multiply the number of gallons by 16 to get the number of cups of fruit juice.
Given that Mary has e gallons of fruit juice, the number of cups of fruit juice can be calculated as follows:
Number of cups = e * 16
Next, we divide the total number of cups of fruit juice by the amount required per serving, which is 1/2 cup:
Number of servings = (Number of cups) / (Amount per serving)
Number of servings = (e * 16) / (1/2)
To simplify this division, we can multiply by the reciprocal of 1/2, which is 2/1 or simply 2:
Number of servings = (e * 16) * (2/1)
Number of servings = 32e
Therefore, the greatest number of servings of punch Mary can make with e gallons of fruit juice is 32e.