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A certain factory produces and sells
x kilograms of ice cream per month. It costs
c dollars to produce one kilogram of ice cream, which is then sold for 0.16 dollars. The factory's monthly net profit is
P dollars.
Write an equation that relates
x,c, and
P.

A certain factory produces and sells $x$ kilograms of ice cream per month. It costs $c$ dollars to produce one kilogram of ice cream, which is then sold for $\mathbf{0 . 1 6}$ dollars. The factory's monthly net profit is $P$ dollars. $\newline$ Write an equation that relates $x, c$ , and $P$ .

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Write and solve equations for proportional relationships

Full solution

Q. A certain factory produces and sells

x

kilograms of ice cream per month. It costs

c

dollars to produce one kilogram of ice cream, which is then sold for

\mathbf{0 . 1 6}

dollars. The factory's monthly net profit is

P

dollars.

\newline

Write an equation that relates

x, c

, and

P

.

Calculate Total Revenue: To find the net profit, we need to subtract the total cost from the total revenue.
Calculate Total Cost: Total revenue is the amount of money made from selling the ice cream, which is $x$ kilograms times the selling price, $0.16$ dollars per kilogram. $\newline$ So, total revenue = $0.16x$ dollars.
Calculate Net Profit: Total cost is the amount of money it takes to produce the ice cream, which is $x$ kilograms times the cost to produce one kilogram, $c$ dollars. $\newline$ So, total cost = $cx$ dollars.
Substitute into Net Profit Equation: Net profit $P$ is total revenue minus total cost. $\newline$ So, $P = (\text{total revenue}) - (\text{total cost})$ .
Substitute into Net Profit Equation: Net profit $P$ is total revenue minus total cost. $\newline$ So, $P = (\text{total revenue}) - (\text{total cost})$ .Substitute the expressions for total revenue and total cost into the net profit equation. $\newline$ $P = (0.16x) - (cx)$ .

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