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A certain factory produces and sells 8000 cars per month, making a monthly net profit of
P dollars. They sell each car for
n dollars and it costs them
c dollars to produce a single car.
Write an equation that relates
P,
n, and
c.

A certain factory produces and sells $8000$ cars per month, making a monthly net profit of $P$ dollars. They sell each car for $n$ dollars and it costs them $c$ dollars to produce a single car. $\newline$ Write an equation that relates $P$ , $n$ , and $c$ .

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Write and solve equations for proportional relationships

Full solution

Q. A certain factory produces and sells

8000

cars per month, making a monthly net profit of

P

dollars. They sell each car for

n

dollars and it costs them

c

dollars to produce a single car.

\newline

Write an equation that relates

P

,

n

, and

c

.

Define variables: Let's define the variables: $\newline$ - $P$ is the monthly net profit. $\newline$ - $n$ is the selling price per car. $\newline$ - $c$ is the cost to produce a single car. $\newline$ - The number of cars produced and sold per month is $8000$ . $\newline$ The net profit is calculated by subtracting the total cost of production from the total revenue. $\newline$ Total revenue is the number of cars sold multiplied by the selling price per car. $\newline$ Total cost is the number of cars produced multiplied by the cost to produce a single car. $\newline$ Let's calculate the total revenue: $\newline$ Total revenue = Number of cars sold $*$ Selling price per car $\newline$ Total revenue = $8000 \times n$
Calculate total revenue: Now, let's calculate the total cost: $\newline$ Total cost = Number of cars produced $*$ Cost to produce a single car $\newline$ Total cost = $8000 \times c$
Calculate total cost: Next, we will write the equation for the net profit: $\newline$ Net profit $P$ = Total revenue - Total cost $\newline$ $P = (8000 \times n) - (8000 \times c)$
Write net profit equation: We can simplify the equation by factoring out the common factor, which is $8000$ : $\newline$ $P = 8000 \times (n - c)$ $\newline$ This is the equation that relates the monthly net profit $P$ , the selling price per car $n$ , and the cost to produce a single car $c$ .

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