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A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets, they were still at a net loss of
$800 (due to the production costs). They sold each ticket for
$70.
Let
y represent the net profit (in dollars) when they have sold
x tickets.
Complete the equation for the relationship between the net profit and number of tickets sold.

y=◻

A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling $10$ tickets, they were still at a net loss of $\$ 800$ (due to the production costs). They sold each ticket for $\$ 70$ . $\newline$ Let $y$ represent the net profit (in dollars) when they have sold $x$ tickets. $\newline$ Complete the equation for the relationship between the net profit and number of tickets sold. $\newline$ $y=\square$

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Evaluate two-variable equations: word problems

Full solution

Q. A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling

10

tickets, they were still at a net loss of

\$ 800

(due to the production costs). They sold each ticket for

\$ 70

.

\newline

Let

y

represent the net profit (in dollars) when they have sold

x

tickets.

\newline

Complete the equation for the relationship between the net profit and number of tickets sold.

\newline

y=\square

Define variables and problem: Let's define the variables and understand the problem. We know that after selling $10$ tickets, the charity organization is at a net loss of $\$800$ . Each ticket is sold for $\$70$ . We need to find the equation that represents the net profit $y$ when $x$ tickets are sold.
Calculate total revenue: To find the equation, we first calculate the total revenue from selling $x$ tickets. The revenue from selling $x$ tickets is $\$70$ times the number of tickets sold, which is $\$70x$ .
Incorporate net loss: Next, we need to incorporate the net loss of $\$800$ into our equation. Since the organization is starting with a loss, this amount needs to be subtracted from the revenue to find the net profit. Therefore, the net profit $y$ can be calculated by subtracting $\$800$ from the total revenue, which gives us the equation $y = 70x - 800$ .

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