Question

A coffee distributor needs to mix a(n) Organic Free Trade coffee blend that normally sells for $8.30 per pound with a Rift Valley coffee blend that normally sells for $13.90 per pound to create 80 pounds of a coffee that can sell for $10.82 per pound. How many pounds of each kind of coffee should they mix?
Answer: They must mix
_____ pounds of the Organic Free Trade Blend
______ pounds of the Rift Valley Blend.
Round your answers to the nearest whole number of pounds.

Answer 1

Answer:

They must mix

_44_ pounds of the Organic Free Trade Blend

_36__ pounds of the Rift Valley Blend.

Round your answers to the nearest whole number of pounds.

Step-by-step explanation:

The formula you are using is:

Total price * total amount= Organic price * amount organic + Rift price * amount rift

First we will simplify it by calculating it for each pound of final mix.

So this is 10.82 * 1 = 8.30 * x + 13.90 * y.

Since the total amount should be 1 pound, you could say that x+y = 1, or that y = 1-x.

If you fill this in you get

10.82 * 1 = 8.30 * x + 13.90 * (1-x)

Which you can solve as follows.

10.82 * 1 = 8.30 * x + 13.90 - 13.90x

10.82 = 13.90 - 5.6x

-5.6x = -3.08

x = -3.08/-5.6 = 0.55

So you will need 0.55 of Organic coffee for each pound of the final mix.

So in total you will need 0.55 * 80 = 44 pounds of Organic coffee.

So you need 80 - 44 = 36 pounds of Rift Valley Coffee.