A coffee distributor needs to mix a(n) Arabian Mocha coffee blend that normally sells for

Question

A coffee distributor needs to mix a(n) Arabian Mocha coffee blend that normally sells for $8.50 per pound with a Kona coffee blend that normally sells for $14.70 per pound to create 30 pounds of a coffee that can sell for $9.95 per pound. How many pounds of each kind of coffee should they mix?

Answer 1

14.7x + 8.5(30-x) = 9.95(30) = 298.50

6.2x = 298.5 -8.5(30) = 298,5- 255 = 43.5

x = 43.5/6.2 = slightly over 7 lbs of $14.70 Kona

slightly less than 23 lbs of $8.50 Arabian

8.5 is within 1.45 of 9.95

14.7 is within 4.75 of 9.95

4.75/1.45 = about 3.3

23/7 = about 3.3

14.7(30-x) + 8.5x = 30(9.95) = 298.5

14.7(30) - 14.7x + 8.5x = 298.5

441 -6.2x = 298.5

6.2x = 441-298.5 = 142.5

x = 142.5/6.2 = 22.984 lbs of $8.50 Arabian

30-x = 7.016 lbs of $14.70 Kona

7.016 pounds of Kona

22.984 pounds of Arabian, rounded off to 3 decimal places