Pregunta
A charity organization is having a fundraiser. \( P \) represents the fundraiser's profit (in dollars) if \( n \) tickets are sold. A negative profit means the expenses exceeded the income from tickets. \( P=70 n-1500 \) What are the expenses of the fundraiser? \( \$ \)
Ask by Guzman Sherman. in the United States
Jan 25,2025
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The expenses of the fundraiser are \$1,500.
Solución
To determine the expenses of the fundraiser, let's analyze the given profit equation:
\[ P = 70n - 1500 \]
Where:
- \( P \) represents the profit in dollars.
- \( n \) is the number of tickets sold.
- \( 70n \) represents the total income from ticket sales (assuming each ticket is sold for \$70).
- \( 1500 \) represents the fixed expenses of the fundraiser.
The profit equation can be understood as:
\[ \text{Profit} = \text{Income} - \text{Expenses} \]
Substituting the provided values:
\[ 70n - 1500 = 70n - \text{Expenses} \]
By comparing both sides of the equation, it's clear that:
\[ \text{Expenses} = \$1500 \]
**Therefore, the expenses of the fundraiser are \$1,500.**
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Simplifique esta solución Bonus Knowledge
The expenses of the fundraiser can be determined from the profit equation \( P = 70n - 1500 \). Here, \( 1500 \) represents the fixed costs or expenses that must be covered regardless of ticket sales. So, the expenses of the fundraiser amount to \( \$1500 \). To find out how it all works, consider that every ticket sold adds \( \$70 \) to the profit. If not enough tickets are sold and \( P \) becomes negative, it means the income from the tickets (which is \( 70n \)) isn't sufficient to cover that \( \$1500 \) expense. So, the fundraiser needs to sell at least \( 22 \) tickets to break even!
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