SOLUTION: Having a terrible problem trying to solve this question: The school board plans to merge two junior high schools into one school of 800 students in which 40% of the students wil

Question 104331: Having a terrible problem trying to solve this question:
The school board plans to merge two junior high schools into one school of 800 students in which 40% of the students will be Caucasian. One of the schools currently has 58% Caucasian students, the other has only 10 % Caucasian students. How many students are in each of the two schools?
Could it be that one school has 464 Caucasian students and the other school has 80 Caucasian students?
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(48558) (Show Source):
You can put this solution on YOUR website!
The school board plans to merge two junior high schools into one school of 800 students in which 40% of the students will be Caucasian. One of the schools currently has 58% Caucasian students, the other has only 10 % Caucasian students. How many students are in each of the two schools?
Could it be that one school has 464 Caucasian students and the other school has 80 Caucasian students?
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1st school DATA:
Let number of students = "x" ; # of whites = 0.58x
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2nd school DATA:
Number of students = "800-x" ; # of whites = 0.10(800-x) = 80-0.10x
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Merged-school DATA:
Number of students = 800 ; # of whites = 0.40(800)=320
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EQUATION:
white + white = white
0.58x + 80-0.10x = 320
0.48x = 240
x = 500 (# of students from the school with 58% Caucasian)
800-x=300 (# of students from the school with 10% Caucasian)
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Cheers,
Stan H.

Answer by Earlsdon(6103) (Show Source):
You can put this solution on YOUR website!
First. let's find the number of caucasian students in the new school.
C = 40% of 800
C = 0.4(800)
C = 320 This is the total number of caucasian students in the new school and you know that this number is made up of 58% of the students from one of the old schools, (so let's call this 58% of x where x is the number of students in this scool) plus 10% of the students in the second school (let's call this 10% of y where y is the number of students in this school).
We can write an equation, but first,realise that x+y = 800 or we can write this as:
y = 800-x Here's the equation we need to solve for x, the number of students in the first school:
1) 0.58x + 0.1(800-x) = 320 The sum of the caucasian students in the old schools is 40% of the total student in the new school or (0.4(800) = 320).
Simplify equation 1) and solve for x.
0.58x + 80 - 0.1x = 320
0.48x = 240
x = 500 This the number of students in the first school.
800-x = 800-500 = 300 This is the number of students in the second school.
Check:
58% of 500 + 10% of 300 = 290 + 30 = 320