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` .

So,

`Profit = 5/3x - 5/4x`

Substitute too the given profit.

`100=5/3x-5/4x`

To simplify the equation, multiply both sides by the LCD of the two fractions which is 12.

`12*100=(5/3x-5/4x)*12`

`1200=20x - 15x`

`1200=5x`

Then, isolate x. To do so, divide both sides by 5.

`1200/5=(5x)/5`

`240=x`

**Hence, we need to sell 240 cards in order to have a profit of
$100.**

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