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During the youth baseball season, Carter grills and sells hamburgers and hot dogs at the Hillview baseball field. On Saturday, he sold $30$ hamburgers and $25$ hot dogs and earned a total of $\$195$ . On Sunday, he sold $15$ hamburgers and $20$ hot dogs and earned a total of $\$120$ . $\newline$ This system of equations can be used to represent the situation. $\newline$ $\newline$ Complete the sentence. $\newline$ How much does Carter charge for a hot dog? $\newline$ $\$$ ____

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Evaluate two-variable equations: word problems

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Q. During the youth baseball season, Carter grills and sells hamburgers and hot dogs at the Hillview baseball field. On Saturday, he sold

30

hamburgers and

25

hot dogs and earned a total of

\$195

. On Sunday, he sold

15

hamburgers and

20

hot dogs and earned a total of

\$120

.

\newline

This system of equations can be used to represent the situation.

\newline

\newline

Complete the sentence.

\newline

How much does Carter charge for a hot dog?

\newline

\$

____

Define Prices: Let's define the price of a hamburger as $h$ dollars and the price of a hot dog as $d$ dollars. From the problem, we have two equations based on Carter's sales: $\newline$ $1$ . $30h + 25d = 195$ (Saturday's sales) $\newline$ $2$ . $15h + 20d = 120$ (Sunday's sales)
Simplify Equations: To simplify, we can divide the second equation by $5$ : $\newline$ $3h + 4d = 24$
Eliminate h: Now, let's eliminate $h$ by multiplying the simplified equation by $10$ and the first equation by $-3$ : $\newline$ $30h + 40d = 240$ $\newline$ $-90h - 75d = -585$
Add Equations: Adding these equations to eliminate $h$ : $\newline$ $-35d = -345$
Solve for d: Solving for $d$ : $\newline$ $d = \frac{-345}{-35} = 9.857$

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