An herbalist has 30 oz of herbs costing $2 per ounce. how many ounces of herbs costing $1 per ounce should be mixed with these 30 ounces of herbs to produce a mixture costing $1.60 per ounce?

30x2+Ax1=(30+A)1.6

60+A=48+1.6A or 0.6A=12 or A=20.
Total mix=50oz and cost=30*2+20=80$
Or 80/50=1.6$/oz.

To find the solution to this problem, we can set up an equation based on the given information. Here's how we can do it step by step:

Let's assume the number of ounces of herbs costing $1 per ounce that should be mixed with the 30 ounces of herbs is x.

1. Firstly, let's calculate the cost of the 30 ounces of herbs costing $2 per ounce. Since each ounce costs $2, the total cost of these herbs will be 30 * $2 = $60.

2. Next, we need to determine the cost of the mixture when it is sold at $1.60 per ounce. This can be found by multiplying the total number of ounces in the mixture by the average cost per ounce. The total number of ounces in the mixture will be 30 + x (30 ounces of $2 herbs plus x ounces of $1 herbs). Therefore, the total cost of the mixture will be (30 + x) * $1.60.

3. Since the mixture needs to have an average cost of $1.60 per ounce, we can set up an equation:

[(30 + x) * $1.60] = ($60 + ($1 * x))

4. Now, let's solve the equation for x to find the number of ounces of herbs costing $1 per ounce that should be mixed with the 30 ounces of $2 per ounce herbs:

Distribute the $1.60 on the left side: 48 + 1.60x = 60 + x

Subtract x from both sides: 0.60x = 12

Divide both sides by 0.60: x = 20

Therefore, to produce a mixture with an average cost of $1.60 per ounce, the herbalist should mix 20 ounces of herbs costing $1 per ounce with the 30 ounces of herbs costing $2 per ounce.