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Yusef earned a total of $n$ dollars from drawing $x$ identically-priced pictures at a festival. Write an equation to describe the relationship between $x$ , the number of pictures, and $n$ , the total earnings.

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Write a linear function: word problems

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Q. Yusef earned a total of

n

dollars from drawing

x

identically-priced pictures at a festival. Write an equation to describe the relationship between

x

, the number of pictures, and

n

, the total earnings.

Identify variables: Identify the variables. $\newline$ Let $n$ = number of pictures Yusef draws. $\newline$ Let $E$ = total earnings from the pictures.
Determine price per picture: Determine the price per picture. $\newline$ Since Yusef earns a total of $E$ dollars from $n$ identically-priced pictures, the price per picture is $\frac{E}{n}$ .
Write equation: Write the equation. $\newline$ The total earnings $E$ is the product of the price per picture and the number of pictures. $\newline$ So, $E = \text{price per picture} \times n$ . $\newline$ But we have a problem here, we can't use $E/n$ as the price per picture because we don't know $E$ or $n$ yet. We need a different variable for the price per picture.

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