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.

Explanation:

We are given the following in the question:

Chamomile tea:

Unit cost = 18.20 per pound

Amount = x pounds

Total cost =

`18.20* x = 18.20x`

Orange tea:

Unit cost = 12.25 per pound

Amount = 12 pounds

Total cost =

`12.25* 12 = 147`

Total mixture:

Unit cost = 14.63 per pound

Amount = (12+x) pounds

Total cost =

`14.63* (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.