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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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Write a linear function: word problems

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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

Determine fixed loss and revenue: Determine the fixed loss and the revenue per ticket. $\newline$ The charity organization is at a net loss of $\$800$ after selling $10$ tickets. This means that the fixed production costs are more than the revenue from these $10$ tickets by $\$800$ . Each ticket is sold for $\$70$ .
Calculate fixed production costs: Calculate the fixed production costs. $\newline$ Since they are at a net loss of $\$800$ after selling $10$ tickets, we can calculate the production costs by adding the loss to the revenue from the $10$ tickets. $\newline$ Production costs = Revenue from $10$ tickets + Net loss $\newline$ Production costs = $(10 \times \$70) + \$800$ $\newline$ Production costs = $\$700 + \$800$ $\newline$ Production costs = $\$1500$
Write equation for net profit: Write the equation for net profit. $\newline$ The net profit $y$ when $x$ tickets are sold is the total revenue from selling $x$ tickets minus the fixed production costs. $\newline$ Net profit ( $y$ ) = Revenue from $x$ tickets - Production costs $\newline$ Net profit ( $y$ ) = ( $x \times \$70$ ) - $\$1500$
Simplify equation for net profit: Simplify the equation for net profit. $\newline$ The equation from the previous step is already in its simplest form. $\newline$ $y = 70x - 1500$

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