Question

In the math department, 20 people ride bikes to work and carry their lunches, 32 people carry their lunches and 35 people ride bikes to work or carry their lunches. How many people ride bikes to work?

Answer 1

2

Explanation:

total of people who ride bikes is 55-32

 23

Answer 2

Answer: 23

Work Shown

A = set of people who ride bikes to work

B = set of people who carry their lunches

n(A) = number of people who ride bikes to work

n(B) = number of people who carry lunches

The goal is to calculate n(A)

We have this given info

• n(B) = 32
• n(A and B) = 20
• n(A or B) = 35

We'll use the formula below to solve for n(A)

n(A or B) = n(A) + n(B) - n(A and B)

35 = n(A) + 32 - 20

35 = n(A) + 12

n(A) = 35-12

n(A) = 23

There are 23 people who bike ride to work.

The venn diagram is shown below. The value x outside of the circles represents the unknown number of people who neither bike ride nor carry their lunches. The values 3 and 20 are inside the "bike riders" circle, so we have a total of 3+20 = 23 bike riders