Answer:
The store should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian cofee.
Step-by-step explanation:
Let "b" be the amount of Brazilian coffee, in pounds, required for the blend and "c" the amount of Colombian coffee required, in pounds.
Since there are two unknown variables a two-equation system is needed to solve the problem, we can set up one equation for weight and another for price as follows:
[tex]b+c=150\\10*b+14*c=11*150[/tex]
Solve for "c" by multiplying the first equation by -10 and adding it to the second one:
[tex]b+c=150\\10b+14c -10b-10c=11*150 -(10*150)\\4c=150\\c = 37.5[/tex]
Now, solve for b by replacing the value obtained into the first equation
[tex]b+c=150\\b= 150 - 37.5\\b=112.5[/tex]
The store should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian cofee.
