Each month a retailer sells 100 identical items.
Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
Answer/Solution
157
Steps/Work
For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 16% of the cost:
Sell Price = Cost + $20
Sell Price = $125 + $20
Thus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...
100($20) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(145) = $7.25 discount
$137.75 = $125 + $12.75
Now, the retailer makes a profit of just $12.75 per item sold.
To earn $2,000 in profit, the retailer must sell....
$12.75(X) = $2,000
X = 2,000/12.75
X = 156.8627 =157 items
A
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 16% of the cost:
Sell Price = Cost + $20
Sell Price = $125 + $20
Thus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...
100($20) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(145) = $7.25 discount
$137.75 = $125 + $12.75
Now, the retailer makes a profit of just $12.75 per item sold.
To earn $2,000 in profit, the retailer must sell....
$12.75(X) = $2,000
X = 2,000/12.75
X = 156.8627 =157 items
A