Question

How many pounds of chamomile tea that costs $18.50 per pound must be mixed with 18 lb of orange tea that costs $12.23 per pound to make a mixture that costs $14.32 per pound?

Answer 1

The amount of chamomile tea that has to be used in order to obtain a mixture that costs $14.32 per pound is 8.997 pounds

Explanation:

In order to find out the amount of chamomile tea that must be used in the mixture to obtain a 14.32 $ per pound, we can use an weighted average where the price points for each kind of tea are the weights and "c" is the amount of chamomile that we have to use in order to obtain the price per pound that we want. So we have:

(18.5*c + 12.23*18)/(c + 18) = 14.32

18.5*c + 220.14 = 14.32*(c+18)

18.5*c + 220.14 = 14.32*c + 257.76

18.5*c - 14.32*c = 257.75 - 220.14

4.18*c = 37.61

c = 8.997 lb