Question

Part I. Venn Diagrams

1. What do you think the two categories would be for this scenario?
For the away RHS football game, 180 students rode the bus out of 400 total students that attended. 115
students were freshmen. There are 25 freshmen that did not ride the bus.

2. What do you think the two categories would be for this scenario?
During C lunch at RHS on Thursday 168 students bought pizza out of the 350 total students that were at C
lunch. 123 students were sophomores. There are 32 sophomores that did not buy pizza.

Answer 1

See explanation

Explanation:

1. 400 students in total.

Category 1: Students which rode the bus (180)

Category 2: Students that were freshmen (115)

Let x be the number of students in both categories. Then

• 180 - x students rode the bus and were not freshmen
• 115 - x students were freshmen and didn't ride the bus

So, 115 - x = 25

x = 90

Thus,

• 90 students rode the bus and were freshmen
• 90 students rode the bus and were not freshmen
• 25 students were freshmen that did not ride the bus
• 400 - 90 - 90 - 25 = 195 students didn't rode the bus and were not freshmen

2. 350 students in total.

Category 1: Students bought pizza (168)

Category 2: Students that were sophomores (123)

Let x be the number of students in both categories. Then

• 168 - x students that bought pizza and were not sophomores
• 123 - x students were sophomores and didn't buy pizza

So, 123 - x = 32

x = 91

Thus,

• 91 students bought pizza and were sophomores
• 77 students bought pizza and were not sophomores
• 32 students were sophomores that did not buy pizza
• 350 - 91 - 77 - 32 = 150 students didn't buy pizza and were not sophomores