Coffee Distribution

Question

A coffee distributor needs to mix a(n) Terraza coffee blend that normally sells for $11.20 per pound with a Guatemala Antigua coffee blend that normally sells for $14.70 per pound to create 80 pounds of a coffee that can sell for $12.56 per pound. How many pounds of each kind of coffee should they mix?

They must mix _____ pounds of Tezera Blend and _______ pounds of Guatemala Antigua Blend

Round to nearest whole number of pounds.

Answer 1

about 48.9 pounds of $11.20 per pound Terraza mixed with about 31.1 pounds of $14.70 per pound Antigua will yield a mixture of 80 pounds of $12.56 per pound blend. Rounded off to nearest 1/10 of a pound

$11.20 mixed with $14.70 to get 80 pounds of $12.56

let x = the amount of $11.20, and 80-x = the amount of $14.70

11.2x + 14.7(80-x) = 12.56(80) = 1004.8

11.2 -14.7x = (12.56-14.7)(80) = - 107/50)(80) = -107(8)/5 =

11.2- 14.7x = 1004.8 - 14.7(80) = -856/5 =-171.2

-3.5x = - 1004.8- 1176 = - 171.2

x = 171.2/3.5 = 1712/35 = about 48.9 pounds of $11.20

80-48.9 = 31.1 pounds of $14.70

a check on the answer or an alternative method is:

11.2 is within 1.36 of 12.56

14.7 is within 2.14 of 12.56

to get a mixture of 12.56 requires more of 11.2 than 14.7, 2.14/1.36 = 107/68 = about 1.57 times more $11.20 than $14.70

2.14/1.26 = 48.9/31.1 = about 1.57

Answer 2

Use the mixture formula: Original Amount + Added Amount = New Amount

Let original amount (Terraza Coffee) be x.

Then let the added amount (Guatemala Antigua coffee) be 80 - x

The formula then looks like this: Original Amount + Added Amount = New Amount

11.20 x + 14.70 (80 - x) = 12.56 (80)

Notice the dollars per pound is multiplied by the number of pounds to get the total dollars for each amount.

Now using your algebra to simplify: 11.20 x + 14.70(80) - 14.70 x = 1004.8

11.20 x + 1176 - 14.70 x = 1004.8

-3.5 x + 1176 = 1004.8

-3.5 x = -171.2

x = 49 lbs

So the amount of Terraza coffe is 49 lbs and the amount of Guatemala Antigua coffee is 31 lbs.