Question

Suppose Albers Elementary School has 44 teachers and Bothel Elementary School has 74 teachers. If the total number of teachers at Albers and Bothel combined is 87, how many teachers teach at both schools?

Answer 1

Answer: 31

Step-by-step explanation:

This is solved Using the theory of sets.

Teachers in Albers school = 44

Teachers in Bothel school = 74

Let the number of teachers that work in both schools be denoted as "x"

This implies that:

Number of teachers in Albers only = 44 - x

Number of teachers in Bothel only = 74 - x

And total number of teachers in both schools = 87,

then

x + (44-x) + (74-x) = 87

118 -x = 87

31 = x

This means the number of teachers that teach in both schools = 31.

Answer 2

Answer: 31 teachers teach at both schools.

Let:

A =  Albers Elementary School

B = Bothel Elementary School

According to the question:

n(A) = 44, n(B) = 74, n(A U B) = 87.

Using the union formula we get:

$n(A \cup B) = n(A)+n(B)-n(A \cap B)\\87 = 44+74-n(A \cap B)\\n(A \cap B)=44+74-87\\n(A \cap B)=31$

So, 31 teachers teach at both schools.

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