Question 761892
Step 1: In the combination of 100 pounds, let there be x pounds of Arabic.
Step 2: So, the combination has (100 - x) pounds of Brazilian
Step 3: Cost of the mixture = cost of arabic in mix + cost of brazilian in mix

= {{{(15*x + 22*(100-x))}}}
Step 4: But the cost of the mixture is given to be 20 per pound. Or, cost of 100 pounds of mix = {{{20*100 = 2000}}}

Step 5: The values of step 3 and step 4 have to be equal. Hence we have the equation
{{{(15*x + 22(100 - x)) = 2000}}}

Step 6: Solve for x
{{{15*x + 2200 - 22*x = 2000}}}

{{{200 = 7*x}}} {{{x = 200/7}}}

So the mixture has {{{200/7}}} pounds of Arabic and {{{100 - 200/7 =500/7}}} pounds of Brazilian coffee.


:)