suppose you own a card shop. you buy one line o cards at a rate of 4 cards for $5. You plan to sell the cards at a rate of 3 cards for $5. How many cards must you sell in order to make a profit of $100?
Profit = Sale - Cost
100 = (5/3)o - (5/4)o
Simplify and solve for o
To determine how many cards you must sell in order to make a profit of $100, we need to understand the cost and the selling price of the cards.
Let's break down the information provided:
1. Purchase cost: You buy one line of cards (presumably a set or a specific quantity) at a rate of 4 cards for $5. This means the cost of 4 cards is $5.
2. Selling price: You plan to sell the cards at a rate of 3 cards for $5. This means you will receive $5 for every set of 3 cards sold.
To calculate the profit per set of cards sold, we need to determine the cost per set and the selling price per set.
1. Cost per set:
Since 4 cards cost $5, we can calculate the cost per set by multiplying the cost of 4 cards by the number of sets:
Cost per set = $5 x (1 set / 4 cards) = $5 / 4 = $1.25
2. Selling price per set:
Since 3 cards are sold for $5, we can calculate the selling price per set by multiplying the selling price of 3 cards by the number of sets:
Selling price per set = $5 x (1 set / 3 cards) = $5 / 3 ≈ $1.67
Now we can calculate the profit per set by subtracting the cost per set from the selling price per set:
Profit per set = Selling price per set - Cost per set
Profit per set = $1.67 - $1.25 = $0.42
To make a profit of $100, we divide the total profit by the profit per set:
Number of sets to be sold = Total profit / Profit per set
Number of sets to be sold = $100 / $0.42 ≈ 238.1
Since we can't sell a fractional number of sets, we need to round up to the nearest whole number. Therefore, you would need to sell at least 239 sets of cards to make a profit of $100.