Help with a linear system?

[youdaone]

This is the question:

"On a test, the average mark of those who passed was 89% and those who failed 11%. If the average mark of the 30 students who participated was 75%, how many passed and how many failed?"

What I have so far:
(p is representing the people who passed and f is representing the people who failed)

1. p + f = 30
2. 0.89p + 0.11f = 0.75

I'm not getting a reasonable answer, I don't want the solution, I just need help with getting the linear system, thank you!

 

[Mrspi]

This is the question:

"On a test, the average mark of those who passed was 89% and those who failed 11%. If the average mark of the 30 students who participated was 75%, how many passed and how many failed?"

What I have so far:
(p is representing the people who passed and f is representing the people who failed)

1. p + f = 30
2. 0.89p + 0.11f = 0.75

I'm not getting a reasonable answer, I don't want the solution, I just need help with getting the linear system, thank you!

Remember how you find the average....

average for those who passed = (total of passing scores)/(number of students who passed)

or, in your case,

89 = (total of passing scores) / p
89p = total of passing scores

Do the same kind of thing for the total of failing scores

AND....if the average for all 30 students was 75, then
average for all students = (total for all students)/(number of students),

or

75 = (total for all students) / 30
30*75 = total for all students

Now you can write a CORRECT second equation:

total for passing students + total for failing students = total for all students

89*p + (you fill in this part) = 30*75

 

[soroban]

Hello, youdaone!

There must be a typo . . . the answers are not integers.
Did you strike the "0" instead of the "9"?

On a test, the average mark of those who passed was 89% and those who failed 11%.
If the average mark of the 39 students who participated was 75%,
how many passed and how many failed?

Let \(\displaystyle P\) = number of students who passed.
Let \(\displaystyle F\) = number of students who failed.

First, we have: .\(\displaystyle P + F \:=\;39\)

\(\displaystyle P\) students had an average of 89.
. . Their total is \(\displaystyle 89P.\)
\(\displaystyle F\) students had an average of 11.
. . Their total is \(\displaystyle 11F.\)
\(\displaystyle 39\) students had an average of 75.
. . The grand total is \(\displaystyle 39\cdot75 = 2925\)

Hence, we have: .\(\displaystyle 89P + 11F \:=\:2925\)


This system of equations has: .\(\displaystyle P = 32,\;F = 7\)