Question 172026
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.