We are given a table showing which school subjects are favored by a group of students. We want to predict the number of students out of $400$ that would choose science as their favorite subject. Consider the given table.

Favorite Subject
Subject	Number of Responses
Math	$6$
Science	$3$
English	$4$
History	$7$

Before we can predict that number, we need to determine what the ratio of students who chose science as their favorite subject to the total number of students is. Let's find the total number of students who gave responses by adding up all the entries from the table.

6 + 3 + 4 + 7 = 20

There were

20

students in the considered group. Now we can find the ratio by dividing the number of students who chose science as their favorite subject,

3,

by the total number of students,

20 .

\frac{Students Who Picked Science}{Total Number of Students} = \frac{3}{2 0}

Out of every

20

students asked, we can expect

3

of them to choose science as their favorite subject. Next, we want to predict how many students out of

400

would pick science as their favorite subject. Let's write an equivalent ratio with

400

in the denominator. Notice that

400 = 20 \times 20 .

This means that we can write the equivalent ratio if we multiply both the numerator and the denominator of our original ratio by

20 .

Let's do it!

Assuming that the ratio of the students choosing science to total number of students stays the same, we found the equivalent ratio

60 : 400 .

This means that we can predict that

60

out of

400

students would choose science as their favorite subject.

Alternative Solution

Alternative Solution Process

We can also solve this problem using a bar diagram. Let's make a bar diagram representing $400$ students. We will divide the diagram into $20$ equal parts because we know how many students per group of $20$ prefer science.

We already know that the ratio of students who prefer science to the total number of students is $\frac{3}{2 0},$ so let's mark $3$ out of the $20$ equal parts on our diagram. These parts will represent the students who chose science as their favorite subject.

Finally, we need to determine how many students are included in each of the $20$ equal parts. Since $400 \div 20 = 20,$ each group represents $20$ students.

The number of students who would choose science as their favorite subject is $3$ times a group containing $20$ students. Because of this, we can predict that $20 \times 3 = 60$ out of $400$ students would choose science as their favorite subject!

Exercise