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The following formula is used in economics to find a company's gross profit rate
P, where
S is the net sales and
C is the cost of goods sold.

P=(S-C)/(S)
Rearrange the formula to highlight the cost of goods sold.

C=◻

The following formula is used in economics to find a company's gross profit rate $P$ , where $S$ is the net sales and $C$ is the cost of goods sold. $\newline$ $P=\frac{S-C}{S}$ $\newline$ Rearrange the formula to highlight the cost of goods sold. $\newline$ $C=\square$

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Write exponential functions: word problems

Full solution

Q. The following formula is used in economics to find a company's gross profit rate

P

, where

S

is the net sales and

C

is the cost of goods sold.

\newline

P=\frac{S-C}{S}

\newline

Rearrange the formula to highlight the cost of goods sold.

\newline

C=\square

Multiply by S: To isolate C, we'll first multiply both sides of the equation by S to get rid of the denominator on the right side. This gives us: $\newline$ $P \times S = S - C$
Combine Terms: Next, we want to get all terms involving $C$ on one side of the equation and everything else on the other side. To do this, we'll add $C$ to both sides and subtract $P \times S$ from both sides, which gives us: $\newline$ $C = S - P \times S$
Factor Out S: Now, we can factor out $S$ on the right side of the equation to simplify it further: $\newline$ $C = S(1 - P)$ $\newline$ This is the rearranged formula that highlights the cost of goods sold ( $C$ ) in terms of the gross profit rate ( $P$ ) and net sales ( $S$ ).

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