Question 163847

First start by using the formula of Cost = Amount*Price
We will also need the idea that the amount of Kenyan + the amount of Sumatran will equal the total amount of the mix.

So setting up our mixture problem we get Cost of Kenyan + Cost of Sumatran = Cost of Mix.

Now let's set up some variables. Let x be the number of pounds of Kenyan coffee and y be the number of pounds of Sumatran coffee.

Then x + y = 20 because we are trying to make 20 pounds of the mix.

So using our Cost formula

9.00x + 8.00y = 8.40*20 since we have x-lb at $9.00 per lb and y-lb at $8.00 per lb to make a total of 20 lb at $8.40 per lb.

since x + y = 20 lets solve for y.
by subtracting y from both sides we get y = 20 - x.

substituting 20 - x for y in our cost equation we get 
{{{9.00x + 8.00(20-x)= 8.40*20}}}

Using the distributive property we get
9.00x + 160 - 8.00x = 168
simplifying we get
1.00x + 160 = 168
solving for x gives us x = 8
therefore we need 8 lb of the kenyan coffee.
now we still need the amount of Sumatran so we take 8 + y = 20
and solve for y to get 12 lb of Sumatran coffee. 
So all together we need 8 lb of Kenyan French Coffee costing $9.00 per pound and  12 lb of Sumatran Coffee costing $8.00 per pound to make 20 lb of a mix costing $8.40 per pound.