SOLUTION: I'm sure i can figure this out if you can just tell me how to translate this into a mathematical equation: three-fourths of the students in Math 200 recieved a grade of C on the

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Question 338239: I'm sure i can figure this out if you can just tell me how to translate this into a mathematical equation:
three-fourths of the students in Math 200 recieved a grade of C on their test, and one-fifth recieved an A. if twenty-two more students recieved C's than recieved A's, how many students are in the class?
Thanks!
Found 2 solutions by checkley77, katealdridge:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
3/4x=1/5x+22
3x/4-x/5=22
(3x*5-x*4)/4*5=22
(15x-4x)/20=22 cross multiply.
11x=20*22
11x=440
x=440/11
x=40 ans. for the number of students.
Proof:
3/4*40=1/5*40+22
120/4=40/5+22
30=8+22
30=30

Answer by katealdridge(100) (Show Source):
You can put this solution on YOUR website!
Let y = the total number of students in Math 200. Let , . This is essentially a proportion problem. Change the fractions into equivalent ones with common denominators.
, . This leaves another unaccounted for. Let's call that B,(it doesn't really matter). So the grades in the class are in the proportion 4:1:15, (A:B:C)
Whenever you want to solve a proportion problem, take the proportion numbers, multiply each of them by x and add them together:
Now it's time to take into account the next piece of info:22 more students got Cs than As. So we can change the C part of the equation (15x) into 4x+22. Now substitute that into the equation:
Solve for x.

Now substitute 2 for x in the equation . You get .
There are 40 students in Math 200.
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