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jasenka [17]
3 years ago
15

Part I. Venn Diagrams

Mathematics
1 answer:
Ann [662]3 years ago
4 0

Answer:

See explanation

Step-by-step 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

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