Page 607 / Exercise 18
The Java Joint wishes to mix organic Kenyan coffee beans that sell for $7.25
per pound with organic Venezuelan coffee beans that sell for $8.50 per pound in
order to form a 50-lb batch of Morning Blend that sells for $8.00 per pound. How
many pounds of each type of bean should be used to make the blend?
STEPS 1 & 2: # pounds of Kenyan coffee beans = k
# pounds of Venezuelan coffee beans = v
STEP 3:
each “k” sells for $7.25/lb
each “v” sells for $8.50/lb
require 50-lb mixture selling for $8.00/lb
STEP 4:
k + v = 50-lb (equation 1)
&
STEP 5:
multiplying
equation 1 by
$7.25/lb ¼
subtracting ¼
!
×k +
×v =
× 50-lb (equation 2)
×k +
× v = $400 (equation 2 simplified)
×k +
× v = $375 (equation 1 modified)
× v = $25
dividing this result on both sides by $0.75/lb yields...
v = $25 ×
(÷ by a fraction is achieved by multiplying with its reciprocal)
= 20-lb
substituting “20-lb” for “v” into (the original) equation 1 gives...
k + 20-lb = 50-lb
i.e., (after subtracting 20-lb from both sides)
k = 30-lb
Thus, one needs to mix 20-lb of Kenyan coffee beans with 20-lb of Venezuelan coffee beans in
order to obtain the desired “Morning Blend” mixture.