SOLUTION: a school board plans to merge 2 schools into a school of 1000 students of which 42% will be african american. One of the schools has a 10% african american student body and the3 ot

Question 172026: a school board plans to merge 2 schools into a school of 1000 students of which 42% will be african american. One of the schools has a 10% african american student body and the3 other has a 90% african american student body. What is the studen population in each of the two schools?
Found 2 solutions by Earlsdon, josmiceli:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x = the student population of the first school and y = the populationof the second school.
From the problem, you get:
x+y = 1000 Total student body of the combined schools.
0.42(1000) = 420 The number of African-American students in the combined schools.
x(0.1) The number of African-American students in the first school.
y(0.9) The number of African-American students in the second school.
So you have enough informtion to write two equations in two unknowns (x and y).
1) x+y = 1000
2) 0.1x+0.9y = 420 Multiply this one by 10 and rewrite in terms of x only.
2) 10(0.1x+0.9y) = 420 ---> x+9y = 4200 ---> x = 4200-9y Now substitute this for x in the first equation.
1) 4200-9y+y = 1000 Solve for y.
4200-8y = 1000 Subtract 4200 from both sides.
-8y = -3200 Divide both sides by -8
y = 400 and
x = 4200 - 9y
x = 4200-9(400)
x = 4200-3600
x = 600
The first school had 600 students.
The second school had 400 students.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
This is a mixture problem which could be 2 types of coffee beans
or anything else. The key facts are: You end up with 42% African American
and the total population of the 2 schools is 1000.
Let the student population of the 1st school =
Let the student population of the 2nt school =
Given:
(1)
I can write:
(2)

Multiply both sides by
(3)
Now multiply both sides of (1) by
and subtract (1) from (3)
(3)
(1)

And, since

The student populations of the schools were
1st: 600 and 2nd: 400
check answer:
(2)

OK
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