Question

A coffee merchant combines coffee that costs $6 per pound with coffee that costs $3.40 per pound. How many pounds of each should be used to make 26 lb of a blend costing $5.25 per pound?

Answer 1

Solve the linear equation 6p + 3.40(1 - p) = 5.25. p represents the proportion of the coffee that is of the expensive kind.

Answer 2

(You should get p = 71.2 %.)

Answer 3

how did you get this part ? = (1-p) 1?

Answer 4

@JoelSjogren

Answer 5

Which part?

Answer 6

1-p

Answer 7

We want everything in the mixture to be of either kind. Thus the sum of p and what's in parentheses should be 100 % = 1. That's only possible if what's in the parentheses is 1 - p: p + (1 - p) = 1 = 100 %.

Answer 8

Hey! I just came up with an alternative explanation which does not involve proportions. Would you like to hear?

Answer 9

Please!

Answer 10

@JoelSjogren

Answer 11

You need to write two expressions telling the price of 26 lb mixed coffee and then equate them. First, the price is 26 lb * $5.25 / lb = $136.5. Clear?

Answer 12

ok @JoelSjogren

Answer 13

Now suppose you use m pounds of the expensive coffee. How much is left for the cheap coffee? 26 - m pounds.

The price of the expensive coffee is thus m * $6, and the price of the cheap coffee is (26 - m) * $3.40.

In total, the price is $ m * 6 + (26 - m) * 3.40.

Answer 14

So there is your equation. $136.5 = $ m * 6 + (26 - m) * 3.40

Answer 15

(You should get m = 18.5.)