First, let's assign a variable to the number of cards sold. Let it be x.
Then, let's use the formula of profit which is:
Profit = Revenue - Total Cost
Total cost refers to the buying price which is $5 per 4 cards. So if we have x cards, the total cost is $`5/4*x`.
The revenue is the total money earned from selling the cards. Note that the selling price is $5 per 3 cards. So if we have sold x number of cards, then the revenue is $`5/3*x` .
`Profit = 5/3x - 5/4x`
Substitute too the given profit.
To simplify the equation, multiply both sides by the LCD of the two fractions which is 12.
`1200=20x - 15x`
Then, isolate x. To do so, divide both sides by 5.
Hence, we need to sell 240 cards in order to have a profit of $100.