53.1k views
3 votes
The table shows the home state of the 175 high school students who attended a tri-state debate tournament. The ratio of Illinois students to Michigan students was 6:5. How many students were from Indiana?

1 Answer

1 vote

Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:

Illinois students / Michigan students = 6/5

We can simplify this proportion by multiplying both sides by 5:

Illinois students = 6/5 * Michigan students

Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:

Illinois students + Michigan students + Indiana students = 175

We can substitute the expression we obtained for the number of Illinois students into this equation:

6/5 * Michigan students + Michigan students + Indiana students = 175

Multiplying both sides by 5 to eliminate the fraction, we get:

6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875

Combining like terms, we get:

11 * Michigan students + 5 * Indiana students = 875

Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:

Illinois students / Michigan students = 6/5

Substituting the values from the table, we get:

Illinois students / Michigan students = 24/20

Cross-multiplying, we get:

Illinois students * 20 = Michigan students * 24

Simplifying, we get:

Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students

Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.

Substituting this into the equation we obtained earlier, we get:

11 * 29 + 5 * Indiana students = 875

Solving for Indiana students, we get:

5 * Indiana students = 875 - 11 * 29 = 546

Dividing both sides by 5, we get:

Indiana students = 546/5 = 109.2

Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.

Therefore, the answer is 110 students from Indiana.

User Jari Laamanen
by
8.3k points