Sweets Bakery makes fat-free cookies that cost $1.70 each to prepare. Sweets expects 20% of the cookies to be imperfect. Sweets wants a 40% markup on cost and produces 150 cookies. Assume that Sweets can sell the broken cookies for $1.60 each. What should Sweets charge for each cookie??

To determine the price Sweets should charge for each cookie, we need to calculate the total cost to produce the cookies and then apply the desired markup.

First, let's calculate the total cost to produce the cookies. We know that Sweets expects 20% of the cookies to be imperfect, so we need to account for both the perfect and imperfect cookies.

The cost to prepare each cookie is $1.70. Since Sweets produces 150 cookies, the total cost of producing the perfect cookies is:

Cost of perfect cookies = $1.70 * (1 - 20%) * 150

Note: We subtract 20% from 1 to account for the imperfect cookies.

The cost to produce the imperfect cookies is the same as the cost of the perfect cookies since they are made the same way. Therefore, the total cost to produce the imperfect cookies is:

Cost of imperfect cookies = $1.70 * 20% * 150

Now, let's calculate the total cost for both perfect and imperfect cookies:

Total cost = Cost of perfect cookies + Cost of imperfect cookies

Next, Sweets wants a 40% markup on cost, so we need to calculate the selling price with the markup:

Selling price = Total cost * (1 + 40%)

Finally, let's calculate the selling price of each cookie:

Price per cookie = Selling price / Total number of cookies

Plugging in the values and calculating:

1. Calculate the cost of perfect cookies:
Cost of perfect cookies = $1.70 * (1 - 20%) * 150
= $1.70 * 0.80 * 150
= $204

2. Calculate the cost of imperfect cookies:
Cost of imperfect cookies = $1.70 * 20% * 150
= $1.70 * 0.20 * 150
= $51

3. Calculate the total cost:
Total cost = Cost of perfect cookies + Cost of imperfect cookies
= $204 + $51
= $255

4. Calculate the selling price with the markup:
Selling price = Total cost * (1 + 40%)
= $255 * (1 + 40%)
= $255 * 1.40
= $357

5. Calculate the price per cookie:
Price per cookie = Selling price / Total number of cookies
= $357 / 150
= $2.38

Therefore, Sweets should charge $2.38 for each cookie.

cost for x cookies: 1.70x

For a 40% final markup, we need revenue of 1.70x * 1.40
That means for 150 cookies, the selling price p needs to satisfy

(150*0.80)p + (150*0.20)*1.60 = (150*1.70)*1.40
p = 2.575

So, sell the perfect ones for $2.58 each