a profit means revenue is greater than cost. so, to make a profit on x boxes, you need
10x > 750 + 4.25x
Now finish it off
cost $4.25 per box to print, and you will sell the cards at $10 per box. How many boxes must you sell to show
a profit?
10x > 750 + 4.25x
Now finish it off
First, let's calculate the cost per box to print the cards:
$4.25 per box
Now, let's think about the selling price per box:
$10 per box
To calculate the profit per box, we subtract the cost per box from the selling price per box:
$10 - $4.25 = $5.75
Next, let's figure out the total expenses, which includes the cost of supplies:
$750 (supply cost)
Now, we can calculate how many boxes you need to sell to cover the expenses and show a profit:
Total Expenses / Profit per Box = Number of Boxes needed to sell
$750 / $5.75 = 130.43
Since we can't sell a fraction of a box, we round up the number to the nearest whole box:
130.43 ≈ 131
Therefore, you need to sell at least 131 boxes of holiday greeting cards to show a profit. Good luck selling those cards and spreading some holiday cheer!
1. Calculate the total cost:
Total cost = Cost of supplies + Cost of printing
Total cost = $750 + (Cost per box * Number of boxes)
2. Calculate the total revenue:
Total revenue = Selling price per box * Number of boxes
3. Set up the equation:
Total revenue - Total cost = Profit
Let's calculate the total cost first:
Total cost = $750 + (Cost per box * Number of boxes)
Total cost = $750 + ($4.25 * Number of boxes)
Now, let's calculate the total revenue:
Total revenue = Selling price per box * Number of boxes
Total revenue = $10 * Number of boxes
Now, we can set up the equation:
Total revenue - Total cost = Profit
$10 * Number of boxes - ($750 + $4.25 * Number of boxes) = Profit
To find the number of boxes needed to show a profit, we need to set the profit equal to zero and solve for the number of boxes:
$10 * Number of boxes - ($750 + $4.25 * Number of boxes) = 0
Expanding this equation:
$10 * Number of boxes - $750 - $4.25 * Number of boxes = 0
Combining like terms:
$5.75 * Number of boxes - $750 = 0
Now, solve for the number of boxes:
$5.75 * Number of boxes = $750
Number of boxes = $750 / $5.75
Calculating:
Number of boxes = 130.43
Since you cannot sell a fraction of a box, you would need to sell at least 131 boxes to show a profit.
First, let's calculate the total cost:
Cost of supplies = $750
Printing cost per box = $4.25
To find the total printing cost, multiply the printing cost per box by the number of boxes:
Total printing cost = $4.25 * Number of boxes
Now, let's calculate the total revenue:
Selling price per box = $10
To find the total revenue, multiply the selling price per box by the number of boxes:
Total revenue = $10 * Number of boxes
To show a profit, the total revenue must be greater than the total cost. Therefore, we can set up an equation to find the break-even point:
Total revenue - Total cost > 0
Substituting the expressions for total revenue and total cost from above, we get:
($10 * Number of boxes) - ($4.25 * Number of boxes) > $750
Now we can solve this inequality to find the minimum number of boxes needed to show a profit:
$10 * Number of boxes - $4.25 * Number of boxes > $750
$5.75 * Number of boxes > $750
Number of boxes > $750 / $5.75
Now, divide $750 by $5.75 to determine the minimum number of boxes you need to sell to show a profit.