Hazel wants to mix 12 pounds of her special blend coffee that will cost her $12.50 per pound. she uses columbian and sumatra coffees which cost her $9.25 and $14.25 per pound.
write an equation that relates all the quantities
how many pounds of each coffee does she need

Let x be the amount of Columbian coffee in the mixture and y the amount of Sumatra coffee in the mixture, then
x + y = 1 . . . (1)
9.25x + 14.25y = 12.50 . . . (2)

(1) x 9.25 => 9.25x + 9.25y = 9.25 . . . (3)

(2) - (3) => 5y = 3.25 => y = 3.25/5 = 0.65

From (1), x + 0.65 = 1 => x = 1 - 0.65 = 0.35

1 pound of the mixture contains 0.35 Columbian coffee and 0.65 Sumatra coffee
Therefore, 12 pounds of the mixture will contain 0.35 x 12 = 4.2 pounds of Columbian coffee and 0.65 x 12 = 7.8 pounds of Sumatra coffee