The number of right-handed students in a mathematics class is nine times the number of left-handed students. The total number of students in the class is 30. How many right-handed students are in the class? How many left-handed students are in the class?
explain it step by step
Let's start by assigning variables to the unknown quantities in the problem.
Let "R" represent the number of right-handed students.
Let "L" represent the number of left-handed students.
From the problem, we know that the total number of students in the class is 30. So we can write the equation:
R + L = 30
We are also given that the number of right-handed students is nine times the number of left-handed students. So we can write another equation:
R = 9L
Now we have a system of two equations with two variables:
R + L = 30
R = 9L
To solve this system, we can substitute the value of R from the second equation into the first equation:
9L + L = 30
10L = 30
L = 3
Now that we know the number of left-handed students is 3, we can substitute this value back into either of the original equations to solve for R:
R = 9(3)
R = 27
So there are 27 right-handed students and 3 left-handed students in the class.