500 pounds of apples were purchased at $0.35 per pound. The desired markup is 30% based on selling price, but 18% spoilage is expected. What should the selling price per pound be?
Well, with 18% expected spoilage, you might want to consider becoming an apple circus and putting on a show with all those clownish apples. But let's crunch some numbers anyway!
We purchased 500 pounds of apples at $0.35 per pound. This means the total cost of the apples is $0.35 x 500 = $175.
Now, with a desired markup of 30%, we need to calculate the selling price. To do so, we first need to determine the selling price per pound excluding the spoilage.
If we subtract the expected 18% spoilage from the total purchase, the total weight of the apples that will actually be sold is 500 - (0.18 x 500) = 500 - 90 = 410 pounds.
To find the selling price per pound, we divide the total cost ($175) by the total weight of the apples sold (410 pounds): $175 / 410 pounds â $0.42683 per pound.
That's approximately $0.43 per pound. So, the selling price per pound should be around $0.43.
To calculate the selling price per pound, we need to consider the purchase price, the desired markup, and the expected spoilage.
First, let's calculate the total cost of the apples:
Total Cost = Purchase Price per Pound x Total Weight
Total Cost = $0.35/pound x 500 pounds
Total Cost = $175
Now, let's calculate the selling price per pound after the markup:
Markup = Desired Markup Percentage / 100
Markup = 30% / 100
Markup = 0.30
Selling Price per Pound = Purchase Price per Pound + (Purchase Price per Pound x Markup)
Selling Price per Pound = $0.35 + ($0.35 x 0.30)
Selling Price per Pound = $0.35 + $0.105
Selling Price per Pound = $0.455
However, we need to take into account the expected spoilage. To do this, we'll subtract the expected spoilage percentage from 100%:
Percentage for Actual Sales = 100% - Expected Spoilage Percentage
Percentage for Actual Sales = 100% - 18%
Percentage for Actual Sales = 82%
Finally, we'll calculate the adjusted selling price per pound:
Adjusted Selling Price per Pound = Selling Price per Pound / Percentage for Actual Sales
Adjusted Selling Price per Pound = $0.455 / 82%
Adjusted Selling Price per Pound = $0.455 / 0.82
Adjusted Selling Price per Pound â $0.5555
Therefore, the selling price per pound should be approximately $0.5555.
To find the selling price per pound, we need to consider the purchase cost, the desired markup, and the expected spoilage.
1. Calculate the cost of the apples:
The purchase cost is given as $0.35 per pound. Multiply this by the total weight of apples purchased: 500 pounds.
Cost of apples = $0.35/pound * 500 pounds = $175.
2. Calculate the spoilage:
The spoilage is expected to be 18%. Multiply this by the cost of the apples to get the amount of spoilage:
Spoilage = 18% * $175 = $31.50.
3. Subtract the spoilage from the cost:
To determine the effective cost of the apples that will be sold without spoilage, subtract the spoilage amount from the total cost of the apples:
Effective cost = Cost of apples - Spoilage = $175 - $31.50 = $143.50.
4. Calculate the desired markup based on selling price:
The desired markup is 30% of the selling price. We need to find the selling price that includes this markup.
Let x be the selling price per pound. The selling price for the 500 pounds of apples will be 500 * x.
Markup = 30% * (500 * x) = 0.3 * (500 * x) = 150x.
5. Determine the final equation:
The selling price per pound should cover the effective cost of the apples plus the desired markup:
Final equation: Effective cost + Markup = Selling price
$143.50 + $150x = Selling price per pound.
By solving this equation, we can find the selling price per pound.
after spoilage, only 410 lbs remain.
500 lbs cost 175.00
30% markup means that the 410 lbs must sell for $227.50
so, ...