As a fund raiser, your class is making and selling holiday greeting cards. You spend $750 on supplies. It will
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?
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
Well, it seems like your class is really working hard to spread some holiday cheer! Now, let's do some math to figure out how many boxes you need to sell to show a profit.
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!
To show a profit, you need to calculate the total revenue and subtract the total cost.
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.
To determine how many boxes you must sell to show a profit, you need to calculate the total cost and the total revenue.
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.