SOLUTION: The Coffee Counter charges $9.00 per pound for Kenyan French Roast coffee and $8.00 per pound for Sumatran coffee. How much of each type should be used to make a 20-lb blend that s
Question 163847: The Coffee Counter charges $9.00 per pound for Kenyan French Roast coffee and $8.00 per pound for Sumatran coffee. How much of each type should be used to make a 20-lb blend that sells for $8.40 per pound? Answer by kennedysj(5) (Show Source):
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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
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.
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