Question 172026
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 ={{{a}}}
Let the student population of the 2nt school ={{{b}}}
Given:
(1) {{{a + b = 1000}}}
I can write:
(2) {{{(.1a + .9b) / (a + b) = .42}}}
{{{(.1a + .9b) / 1000 = .42}}}
Multiply both sides by {{{1000}}}
(3) {{{.1a + .9b = 420}}}
Now multiply both sides of (1) by {{{.1}}}
and subtract (1) from (3)
(3) {{{.1a + .9b = 420}}}
(1) {{{.1a + .1b = 100}}}
{{{.8b = 320}}}
{{{b = 400}}}
And, since
{{{a + b = 1000}}}
{{{a = 600}}}
The student populations of the schools were
1st: 600 and 2nd: 400
check answer:
(2) {{{(.1a + .9b) / (a + b) = .42}}}
{{{(.1*600 + .9*400) / 1000 = .42}}}  
{{{(60 + 360) / 1000 = .42}}}
{{{420 / 1000 = .42}}}
{{{.42 = .42}}}
OK