Revisiting a problem

Solve a problem using a two-way table

Just as we can use Venn diagrams to solve problems, we can also use two-way tables.

Let’s revisit problem 2 from Solving problems using Venn diagrams¹ to see how a two-way table can help us.

In a class of 27 students, 10 study Italian and 23 study French. If every student studies at least one of these languages, how many students study both Italian and French?

Establishing a variable

Writing expressions

There are 23 students who study French. We already have x of them in our table so we need to add the other 23 – x .


	Studies French	Doesn't study French
Studies Italian	x
Doesn't study Italian	23 – x	0

There are 10 students who study Italian. We already have x of them in our table so we need to add the other 10 – x.


	Studies French	Doesn't study French
Studies Italian	x	10 – x
Doesn't study Italian	23 – x	0

There are 27 students in the class so the four numbers in the table must add to 27.

x + 10 – x + 23 – x = 27

33 – x = 27

x = 6

There are 6 students who study both Italian and French.

Revisiting a problem

Revisiting a problem

Solve a problem using a two-way table

Links