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A certain factory produces and sells
C computers per month. It costs
x dollars to produce a single computer, and the factory sells each computer for
y dollars. Their monthly net profit is 10,000 dollars.
Write an equation that relates
C,
x, and
y.

A certain factory produces and sells $C$ computers per month. It costs $x$ dollars to produce a single computer, and the factory sells each computer for $y$ dollars. Their monthly net profit is $10$ , $000$ dollars. $\newline$ Write an equation that relates $C$ , $x$ , and $y$ .

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Write and solve equations for proportional relationships

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Q. A certain factory produces and sells

C

computers per month. It costs

x

dollars to produce a single computer, and the factory sells each computer for

y

dollars. Their monthly net profit is

10

,

000

dollars.

\newline

Write an equation that relates

C

,

x

, and

y

.

Net Profit Calculation: The net profit for the factory is the total revenue from selling the computers minus the total cost of producing them, with the net profit given as $\$10,000$ . We can express the total revenue as the number of computers sold, $C$ , times the selling price per computer, $y$ . So, the total revenue is $Cy$ .
Total Revenue Calculation: Similarly, the total cost of producing the computers is the number of computers produced, $C$ , times the production cost per computer, $x$ . So, the total cost is $Cx$ .
Total Cost Calculation: The net profit is the total revenue minus the total cost. We can write this as an equation: $\text{Net Profit} = \text{Total Revenue} - \text{Total Cost}$ . Substituting the expressions for total revenue and total cost, we get: $\text{Net Profit} = C_y - C_x$ .
Substituting Net Profit Value: Since the net profit is given as $\$10,000$ , we can substitute this value into the equation. This gives us: $10,000 = C_y - C_x$ .
Factoring Out C in the Equation: To make the equation relate $C$ , $x$ , and $y$ , we can rewrite it by factoring out $C$ from the right side of the equation. This gives us: $10,000 = C(y - x)$ .

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