Patricia and her brother Ian help themselves to a pitcher of lemonade on the kitchen counter. Patricia takes a glass and fills it with p ounces of lemonade. Ian takes a bigger glass and pours himself 20% more lemonade than Patricia poured in her glass. Write an expression to represent the quantity of lemonade (in ounces) in Ian’s glass in terms of the quantity in Patricia’s glass (p).
Complete the steps below to solve the problem.
Part A
Write an expression in terms of p that shows how many more ounces Ian poured in his glass than Patricia poured in hers.
Ian poured 20% more than Patricia, so the quantity of lemonade in Ian's glass is 1.2 times the quantity in Patricia's glass. Therefore:
Quantity in Ian's glass = 1.2p
Quantity in Patricia's glass = p
To find how many more ounces Ian poured, we subtract the quantity in Patricia's glass from the quantity in Ian's glass:
Quantity in Ian's glass - Quantity in Patricia's glass = 1.2p - p = 0.2p
So Ian poured 0.2p more ounces of lemonade than Patricia.
To find out how many more ounces Ian poured in his glass than Patricia poured in hers, we need to calculate 20% of the quantity in Patricia's glass.
Step 1: Convert 20% to decimal form by dividing it by 100:
20 / 100 = 0.2
Step 2: Multiply the quantity in Patricia's glass (p) by 0.2 to find out how many more ounces Ian poured:
0.2 * p = 0.2p
Thus, the expression that shows how many more ounces Ian poured in his glass than Patricia poured in hers is 0.2p.