Revisiting a problem

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 diagrams 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?

We start by drawing a two-way table. Let x be the number of students who study both French and Italian.

Studies French

Doesn't study French

Studies Italian

x

Doesn't study Italian

0

Read the problem carefully and explain why there is a zero in the table.

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.