Linear equaton

Question

Let there be a variable to represent unknown.

In one section of a highschool course, eight times as many students passed the final exam as failed it. If there were 36 students in the section, how many passed the exam

Answer 1

Let x = # who failed; then #who passed is 8x.

Total 9x = 36.  You can take it from here!

Answer 2

P = number of students that passed

 

F = number of students that failed

 

You just need to solve these 2 equations in 2 unknowns P and F:

 

P = 8F

P + F = 36

 

Substitute P = 8F into the second equation and get

 

8F + F = 36 ⇒ 9F = 36 ⇒ F = 4

 

Then P = 8F = 8(4) = 32

 

Therefore, 32 passed and 4 failed.

 

Note the results are consistent with the given information:

 

P + F = 32 + 4 = 36

P = 8F = 8(4) = 32