Mathematic Algebra Thing

Question

A coffee distributor needs to mix a(n) Gualtemala Antigua coffee blend that normally sells for $9.00 per pound with a Ethiopian coffee blend that normally sells for $12.90 per pound to create 100 pounds of a coffee that can sell for $12.24 per pound. How many pounds of each kind of coffee should they mix?

Answer 1

12,9x + 9(100-x) = 100(12.24)

12.9x - 9x = 1224 - 900 = 324

x = 324/3.9= 108/1.3 = about 83 pounds of $12.90

mixed with about 17 pounds of $9.00

or another method

12.9 - 12.24 = .66

12.24 -9 = 3.24

3.24/.66 = 324/66 =108/22 = 54/11 times as much $12.90 as $9

54/11 x 17 = about 83 rounded to nearest integer

54/11 x n = (100-n)

54n = 1100 -11n

65n = 1100

n = 1100/65= about 16.923 pounds of $9

and 83.077 pounds of $12.90