Arabica Coffee Beans
Suppose that you want to blend two coffees in order to obtain a new blend. The blend will be made with the?
best Arabica beans that sell for $9.00 per pound and select African Robustas that sell for $11.50 per pound to obtain 100 pounds of the new blend. The new blend will sell for $10.00 per pound and there will be no difference in revenue from selling the new blend versus selling the beans separately. How many pounds of the Arabica and Robusta beans are required?
60 lbs. Arabica and 40 lbs African Robustas. First, make 2 formulas.
X + Y = 100 (X lbs. of Arabica beans plus Y lbs. of African Robustas equals 100 pounds per blend)
9X + 11.50Y = 1000 ($9/lb of Arabica plus $11.50/lb of African Robustas equals $1000/blend (which, remember is 100 pounds, sold at $10/pound).
use the first equation to solve for the second
X = 100 – Y
9*(100 – Y) + 11.50Y = 1000
900 – 9y + 11.50y = 1000
900 + 2.50y = 1000
2.50y = 100
y = 100/2.50 = 40
Now plug 40 back in for Y (either equation – both will work)
X + 40 = 100
X = 100 – 40 = 60.
Plug both X & Y back into other equation to check
9 * 60 + 11.5 * 40 = 1000
540 + 460 = 1000
1000 = 1000 … yep, you’re good
Fair trade organic coffee Arabica Coffee Beans are Mild
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