Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ A fashion photographer needs to hire a stylist to prepare his models. Santiago charges $\$165$ for showing up, plus $\$78$ per hour. Jenny charges $\$181$ plus $\$74$ per hour. The photographer realizes that, given the expected duration of his photo shoot, either stylist would cost him the same amount. What would the duration be? What would the cost be? $\newline$ If the shoot lasted for _____ hours, either stylist would cost $\$\_\_\_\_\_$ .

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Algebra 2

Solve a system of equations using any method: word problems

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

A fashion photographer needs to hire a stylist to prepare his models. Santiago charges

\$165

for showing up, plus

\$78

per hour. Jenny charges

\$181

plus

\$74

per hour. The photographer realizes that, given the expected duration of his photo shoot, either stylist would cost him the same amount. What would the duration be? What would the cost be?

\newline

If the shoot lasted for _____ hours, either stylist would cost

\$\_\_\_\_\_

Set up equations: Set up the equations based on the given information. $\newline$ Santiago's cost: $\$165$ + $\$78$ per hour. $\newline$ Jenny's cost: $\$181$ + $\$74$ per hour. $\newline$ The costs are the same, so we can set the two expressions equal to each other to find the duration of the photo shoot. $\newline$ Equation: $165 + 78h = 181 + 74h$
Solve for $h$ : Solve for $h$ (the number of hours). $\newline$ Subtract $74h$ from both sides of the equation: $\newline$ $165 + 78h - 74h = 181 + 74h - 74h$ $\newline$ $165 + 4h = 181$
Subtract to isolate variable: Subtract $165$ from both sides to isolate the variable term. $\newline$ $165 + 4h - 165 = 181 - 165$ $\newline$ $4h = 16$
Divide to solve for h: Divide both sides by $4$ to solve for $h$ . $\frac{4h}{4} = \frac{16}{4}$ $h = 4$
Calculate total cost: Calculate the total cost for either stylist by substituting $h$ back into one of the original equations. $\newline$ Using Santiago's cost equation: $165 + 78 \times 4$ $\newline$ $165 + 312 = 477$
Verify cost: Verify the cost with Jenny's cost equation to ensure it is the same. $\newline$ $181 + 74 \times 4$ $\newline$ $181 + 296 = 477$