Question 91968
 

The idea is that the total worth of coffee will remain unchanged before and after mixture.

Let x represent the amount of $9-coffee
    y represent the amount of $12-coffee

then
 x + y = 100
 9x +  12y = 11.25 * 100 = 1125

so we have 

x + y = 100
9x +  12y = 1125

multiply -9 on both sides of first equation
-9x - 9y = -900

add to second equation

3y = 225

y =  75 lbs
and x = 100 -75 = 25 lbs

so we need to mix 25 lbs of $9-coffee with 75 lbs of $12-coffee.