Question

Use a system of linear equations with two variables and two equations to solve. 238 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.Passing Students: Failing Students:

Answer 1

Given:

Total number of students = 238

Let the number of passing students be x

We're given that 6 times the number of students passed as failed. Hence, the number of students:

`=\text{ }(x)/(6)`

Hence, we can write:

`\begin{gathered} x\text{ + }(x)/(6)\text{ = 238} \\ \frac{6x\text{ + x}}{6}\text{ = 238} \end{gathered}`

Solving for x:

`\begin{gathered} \text{Cross}-\text{Multiply} \\ 7x\text{ = 238 }*\text{ 6} \\ 7x\text{ = 1428} \\ \text{Divide both sides by 7} \\ x\text{ = 204} \end{gathered}`

Hence the number of passing students is 204 students

We can find the number of failing students by subtraction:

`\begin{gathered} \text{Number of failing students = 238 - 204} \\ =\text{ 34} \end{gathered}`

Answer:

Passing students: 204

Failing students: 34