Question

A coffee distributor needs to mix a(n) Mexican Shade Grown coffee blend that normally sells for $11.80 per pound with a Gualtemala Antigua coffee blend that normally sells for $13.30 per pound to create 10 pounds of a coffee that can sell for $12.25 per pound. How many pounds of each kind of coffee should they mix?

Answer 1

• 7 pounds Mexican Shade Grown
• 3 pounds Guatemala Antigua

Explanation:

You want the number of pounds of each of coffees costing $11.80 per pound and $13.30 per pound are needed to make 10 pounds of a mix costing $12.25 per pound.

Setup

Let g represent the number of pounds of Guatemala Antiqua coffee in the mix. Then 10-g is the number of pounds of Mexican Shade Grown coffee. The total cost of the mix is ...

13.30g +11.80(10 -g) = 10(12.25)

Solution

Simplifying, we get ...

1.50g +118.00 = 122.50

1.50g = 4.50

g = 3

10 -g = 7

Three (3) pounds of Guatemala Antigua coffee blend and seven (7) pounds of Mexican Shade Grown coffee blend should be mixed.

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Additional comment

If you look at where the numbers come from, you see that the generic solution to a mixture problem like this is ...

fraction of highest cost contributor

= ((mix cost) - (lowest cost))/((highest cost) - (lowest cost))

= (12.25 -11.80)/(13.30 -11.80) = 0.45/1.50 = 0.3

That is, the 10# mix will have 0.3·10# = 3# of the highest cost contributor.

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