Question

The Coffee Counter charges $8.00 per pound for Kenyan French Roast coffee and $12.00 per pound for Sumatran coffee.

How much of each type should be used to make a 12 pound blend that sells for $10.00 per pound?

Answer 1

irst 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+%2B+8.00%2820-x%29=+8.40%2A20

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.

Explanation:

Hope this helps.