Linear Equations

Question

Use a system of linear equations with two variables and two equations to solve.

 

259 students enrolled in a freshman-level chemistry class. By the end of the semester, 6 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.

Answer 1

p + f = 259

p = 6f

Can you solve and answer?

Answer 2

Let x denote the number of people who passed the class and let y denote the number of people who failed the class. Because everyone either passed or failed, we know x+y must account for all 259 students.

x + y = 259

By the second sentence, we know x is 6 times the size of y.

x = 6y

Substituting the second equation into the first,

6y + y = 259

7y = 259

y = 37

This means 37 students failed the class and therefore 222 students passed the class.