Question

how many pounds of chamomile tea that costs 18.20 per pound must be mixed with 12lb of orange tea that costs 12.25 per pound to make a mixture that costs 14.63 per pound

Answer 1

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 =

$18.20\times x = 18.20x$

Orange tea:

Unit cost = 12.25 per pound

Amount = 12 pounds

Total cost =

$12.25\times 12 = 147$

Total mixture:

Unit cost = 14.63 per pound

Amount = (12+x) pounds

Total cost =

$14.63\times (12+x) = 175.56 + 14.63x$

We can write the equation that cost of mixture is equal to cost of chamomile tea and orange tea.

$18.20x + 147 = 175.56 + 14.63x\\\Rightarrow 18.20x- 14.63x = 175.56-147\\\Rightarrow 3.57x = 28.56\\\Rightarrow x = 8$

Thus, 8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.