Question

a coffee distributor needs to mix a costa rican coffee blend that normally sells for $8.00 per pound with an organic free trade coffee blend that normally sells for $13.00 per pound to create 90 pounds of a coffee that can sell for $8.22 per pound. how many pounds of each kind of coffee should they mix

Answer 1

Let a pound of costa rican coffee be x

Let a pound of organic free coffee be y

x + y = 90

(8x/90) + (13y/90) = 8.22

`\begin{gathered} \frac{8x\text{ + 13y}}{90}=\text{ 8.22} \\ 8x\text{ + 13y = 739.8} \end{gathered}`

Therefore we have two equations, which can be solve simultaneously

x + y = 90 ---------1

8x + 13y = 739.8 -------2

make x subject in equation 1

x = 90 -y

substitute x = 90 - y in equation 2

8 ( 90 -y ) + 13y = 739.8

720 - 8y + 13y = 739.8

5y = 739.8 -720

5y = 19.8

divide through by 5

y = 19.8/5 = 3.95

Substitute y =3.95 in x= 90 - y

x = 90 - 3.95 = 86.04

Thus, 3.95 pounds of organic free coffee ne mixed with 86.04 pounds of costa rican coffee