Let's call the number of pancake breakfasts the Drama Club needs to sell "x".
The total revenue from selling "x" pancake breakfasts can be calculated by multiplying the number of breakfasts by the price per breakfast:
Total revenue = x * $5.25
The total cost of running the pancake breakfast event includes the rental cost of the facility plus the cost of making the pancakes and other expenses. Since we don't know the exact cost of making the pancakes and other expenses, we'll call the total cost "C".
Total cost = $152 + C
The profit can be calculated as the difference between the total revenue and the total cost:
Profit = Total revenue - Total cost
We want the profit to be $1000, so we can set up the following equation:
$1000 = x * $5.25 - ($152 + C)
To solve for "x", we need to isolate it on one side of the equation. First, we can simplify the equation by combining like terms:
$1000 = $5.25x - $152 - C
Next, we can add $152 and "C" to both sides of the equation:
$1152 + C = $5.25x
Finally, we can divide both sides of the equation by $5.25 to solve for "x":
x = ($1152 + C) / $5.25
Since we don't know the exact cost of making the pancakes and other expenses, we can't solve for "x" exactly. However, we do know that the Drama Club needs to sell enough pancake breakfasts to make a profit of $1000. Therefore, we can set up an inequality to represent this:
Total revenue - Total cost ≥ $1000
x * $5.25 - ($152 + C) ≥ $1000
Simplifying this inequality, we get:
x * $5.25 ≥ $1152 + C + $1000
x * $5.25 ≥ $2152 + C
x ≥ ($2152 + C) / $5.25
This means that the Drama Club needs to sell at least ($2152 + C) / $5.25 pancake breakfasts to make a profit of $1000, where "C" is the cost of making the pancakes and other expenses.