Question

how many pounds of chamomile tea that costs $18.12 per pound must be mixed with 18 lb of orange tea that costs $12.25 per pound to make a mixture that costs $14.20 per pound?

Explanation:

Step1: Let the amount of chamomile tea be $x$ pounds.

The amount of orange - tea is 16 pounds.

Step2: Set up the cost - equation.

The cost of chamomile tea per pound is $\$18.12$, the cost of orange - tea per pound is $\$12.25$, and the cost of the mixture per pound is $\$14.20$. The total weight of the mixture is $(x + 16)$ pounds. So, the equation based on the cost - balance is $18.12x+12.25\times16 = 14.20(x + 16)$.

Step3: Expand the right - hand side of the equation.

$18.12x+196=14.20x + 227.2$.

Step4: Move the $x$ terms to one side and the constants to the other side.

$18.12x-14.20x=227.2 - 196$.

Step5: Combine like terms.

$3.92x = 31.2$.

Step6: Solve for $x$.

$x=\frac{31.2}{3.92}\approx7.96$ pounds.

Answer:

Approximately 7.96 pounds