Michael Reeves, an ice cream vendor, pays $17.50 for a five-gallon container of premium ice cream. From this quantity he sells 80 scoops at $0.90 per scoop. If he sold smaller scoops, he could sell 98 scoops from the same container; however, he could charge only $0.80 per scoop. If Michael switches to the smaller scoops, by how much will his profit per container go up or down? (Profit = Sales – Expenses)
Using your answer from the questions above, by what percent will the profit change? (Round to the nearest tenth of a percent.)
cost = $17.50
@80 scoops => 80*($0.90)=$72 revenue
$72-$17.50=$54.50 profit
@98 scoops => 98*($0.80)=$78.40 revenue
$78.40-$17.50 = $60.90 profit
$60.90 - $54.50 = $6.40
profit went up by $6.40
$60.90/$54.50=1.1174
profit went up by 11.74%
To determine the profit per container, we need to calculate the sales and expenses for each scenario.
Scenario 1: Selling 80 scoops at $0.90 per scoop.
Sales = Number of scoops sold * Price per scoop
Expenses = Cost of the container
Sales = 80 * $0.90 = $72
Expenses = $17.50
Profit (Scenario 1) = Sales - Expenses = $72 - $17.50 = $54.50
Scenario 2: Selling 98 scoops at $0.80 per scoop.
Sales = Number of scoops sold * Price per scoop
Expenses = Cost of the container
Sales = 98 * $0.80 = $78.40
Expenses = $17.50
Profit (Scenario 2) = Sales - Expenses = $78.40 - $17.50 = $60.90
So, if Michael switches to smaller scoops, the profit per container will go up by:
Difference in profit = Profit (Scenario 2) - Profit (Scenario 1)
Difference in profit = $60.90 - $54.50 = $6.40
The profit will go up by $6.40 per container if Michael switches to smaller scoops.
To calculate the percent change in profit, we can use the following formula:
Percent change = (Difference in profit / Profit (Scenario 1)) * 100
Percent change = ($6.40 / $54.50) * 100 ≈ 11.7%
Therefore, the profit will increase by approximately 11.7% if Michael switches to smaller scoops.
To find the profit per container for each scenario, we need to calculate the expenses and the sales.
Scenario 1: Selling 80 scoops at $0.90 per scoop.
Expenses: Michael pays $17.50 for a five-gallon container of ice cream.
Sales: Selling 80 scoops at $0.90 per scoop gives us 80 * $0.90 = $72.
Profit = Sales - Expenses = $72 - $17.50 = $54.50.
Scenario 2: Selling 98 scoops at $0.80 per scoop.
Expenses: The expenses remain the same as in the first scenario, which is $17.50.
Sales: Selling 98 scoops at $0.80 per scoop gives us 98 * $0.80 = $78.40.
Profit = Sales - Expenses = $78.40 - $17.50 = $60.90.
Comparing the profits:
Profit in Scenario 1: $54.50
Profit in Scenario 2: $60.90
The profit per container will increase by $60.90 - $54.50 = $6.40 if Michael switches to the smaller scoops.
To find the percentage change in profit, we can use the following formula:
Percentage Change = (New Value - Old Value) / Old Value * 100
Percentage Change = ($6.40 - $54.50) / $54.50 * 100
Percentage Change = -$48.10 / $54.50 * 100
Percentage Change ≈ -88.22%
Therefore, the profit will decrease by approximately 88.2% if Michael switches to the smaller scoops.