Problem of the Week
Problem A and Solution
Pizza Party
Problem
Last year, April had a pizza party for all 36 students in her class. She expected everyone to eat
4 slices of pizza each. When the party was done, she had a lot of pizza left over. April observed
three groups at the party.
•Group A made up one-third of the class. Each person in this group ate half the number
of slices April predicted everyone would eat.
•Group B made up half of the class. They each ate 2 slices. After that, each person
shared one more slice with a friend in this group.
•Group C made up the remainder of the class. Each person in this group ate 4 slices
each, as she expected.
A) How many people were in Group A?
B) How many pizza slices in total did the people in Group B eat?
C) How many people were in Group C?
D) If a large pizza has 12 slices, how many pizzas should April have ordered for the party to
avoid having so much pizza left over? Note that she might still have ended up with a few
extra slices.
Solution
A) Since 1
3of the students were in Group A, and there were 36 people, that
means that there were 36 ÷3 = 12 students in this group.
B) Group B had 1
2of the students in the class, which is equal to
36 ÷2 = 18 people. Each of these people ate 2 slices, for a total of
18 ×2 = 36 slices. Each of these 18 people also split 1 slice. This means that
18 ÷2=9pairs of students shared a single slice of pizza. In total the people
in Group B ate: 36 + 9 = 45 slices of pizza.
C) Between Group A and Group B we have accounted for a total of
12 + 18 = 30 people. The remaining 36 −30 = 6 people were in Group C,
and they ate 4 slices of pizza each.
