8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.
Step-by-step explanation:
We are given the following in the question:
Chamomile tea:
Unit cost = 18.20 per pound
Amount = x pounds
Total cost =
[tex]18.20\times x = 18.20x[/tex]
Orange tea:
Unit cost = 12.25 per pound
Amount = 12 pounds
Total cost =
[tex]12.25\times 12 = 147[/tex]
Total mixture:
Unit cost = 14.63 per pound
Amount = (12+x) pounds
Total cost =
[tex]14.63\times (12+x) = 175.56 + 14.63x[/tex]
We can write the equation that cost of mixture is equal to cost of chamomile tea and orange tea.
[tex]18.20x + 147 = 175.56 + 14.63x\\\Rightarrow 18.20x- 14.63x = 175.56-147\\\Rightarrow 3.57x = 28.56\\\Rightarrow x = 8[/tex]
Thus, 8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.
