Final answer:
To solve the problem, set up a ratio equation using the given ratio of Illinois students to Michigan students. Substitute the value of y into the second equation and solve for y. The number of students from Michigan is approximately 80. Subtract the number of students from Illinois and Michigan from the total number of students to find the number of students from Indiana, which is 15.
Step-by-step explanation:
To solve this problem, we can set up an equation using the given ratio of Illinois students to Michigan students. Let's let x represent the number of Illinois students and y represent the number of Michigan students. According to the ratio, we have:
x/y = 6/5
To find the total number of students, we can add the number of Illinois students and the number of Michigan students together. Since there are 175 students in total, we have:
x + y = 175
Now we have a system of two linear equations with two variables. We can solve this system by substitution or elimination. Let's solve it using substitution. We'll start by solving the first equation for x:
x = (6/5)y
Next, substitute this expression for x into the second equation:
(6/5)y + y = 175
Simplify the equation:
(11/5)y = 175
Multiply both sides by 5/11:
y = (175 * 5) / 11
Approximately, y = 79.55
Since we can't have a fraction of a student, we round up to the nearest whole number:
y = 80
So, there were 80 students from Michigan.
To find the number of students from Indiana, we can subtract the number of students from Illinois and Michigan from the total number of students:
Number of students from Indiana = Total number of students - Number of students from Illinois - Number of students from Michigan
Number of students from Indiana = 175 - x - y
Number of students from Indiana = 175 - (6/5)y - y
Substitute the value of y that we found earlier:
Number of students from Indiana = 175 - (6/5) * 80 - 80
Number of students from Indiana = 15