coffee blend word problem

Question

A coffee distributor needs to mix a(n) Terraza coffee blend that normally sells for $8.40 per pound with a Kona coffee blend that normally sells for $13.60 per pound to create 20 pounds of a coffee that can sell for $11.78 per pound. How many pounds of each kind of coffee should they mix?

(round your answers to the nearest whole number of pounds)

Answer 1

Let x = number of pounds of Terraza coffee

Let y = number of pounds of Kona coffee

Together they will combine to be 20 lbs of coffee.

x + y = 20

Now the total cost of the mixture would be 20 lbs x 11.78 per pound which would be

20 x 11.78. Multiplying that out would give us 235.60.

.

We would then multiple each quantity of coffee by it's cost per pound.

So 8.4x would be the total cost of the Terranze coffee.

And 13.60y would be the total cost of the Kona coffee.

Adding the cost of each together will give us the total cost.

8.4x + 13.6y = 235.60.

Now that we solve for x in terms of y.

So take x + y = 20 and

x = 20 - y

Substituting the value of x with 20 - y in the equation for the total cost and solve that:

8.4(20-y) + 13.6y = 235.6

8.4(20) - 8.4y +13.6y = 235.6

168 - 8.4y + 13.6y = 235.6 .

168 + 5.2y = 235.6

5.2y = 235.6 - 168

5.2y = 67.6

y = 13 or Kona coffee would be 13 lbs

x = 7 or Terreza coffee would be 7 lbs.

Answer 2

Let T = lbs of Terraza coffee & K = lbs of Kona coffee then use a weighted average

{ (8.40)T + (13.6)K }/(T + K) = 11.78 and the second equation is the quanities

T + K = 20

Solving for T & K with the 2 equations gives T = 7 & K = 13