MHB Word problem - Application of linear equations

[paulmdrdo1]

Every freshman student at a particular college is required to take an english aptitude exam. A student who passes the examination enrolls in english composition, and a student who fails the test must enroll in english fundamentals. In a freshman class of 1240 students there are more students enrolled in english fundamentals than in english composition. However, if 30 more students had passed the test, each course would have the same enrollment. how many students are taking each course?

My solution

let $x=$number of students who passed

$1240-x =$ number of students who failed

$x+30=1240-x$

$2x=1240-30$
$2x=1210$
$x=605$

605 students are taking English Composition
635 students are taking English fundamentals

is my solution correct?

thanks!

 

[MarkFL]

I would let $P$ be the number who passed and $F$ be the number who failed. We are given in the problem:

$$P+F=1240$$

$$P+30=F-30$$

Note that if we add 30 to those that passed, then we have to subtract 30 from those that failed. So solve this system...what do you find?

 

[HallsofIvy]

Every freshman student at a particular college is required to take an english aptitude exam. A student who passes the examination enrolls in english composition, and a student who fails the test must enroll in english fundamentals. In a freshman class of 1240 students there are more students enrolled in english fundamentals than in english composition. However, if 30 more students had passed the test, each course would have the same enrollment. how many students are taking each course?

My solution

let $x=$number of students who passed

$1240-x =$ number of students who failed

$x+30=1240-x$

This is incorrect. "If 30 more students had passed the test" then, yes, the number of students who passed and so must take one course is x+ 30 but then the number who failed, and must take the other course would be 30 less: 1240- (x+ 30)= 1210- x.

The equation you want to solve is x+ 30= 1210- x.

$2x=1240-30$
$2x=1210$
$x=605$

605 students are taking English Composition
635 students are taking English fundamentals

is my solution correct?

thanks!