Question

Write a system of equations to describe the situation below, solve using substitution, and filin the blanks.A fashion photographer needs to hire a stylist to prepare her models. Shelby charges $189for showing up, plus $61 per hour. Ava charges $153 plus $79 per hour. The photographerrealizes that, given the expected duration of her photo shoot, either stylist would cost her tosame amount. What would the cost be? What would the duration be?

Answer 1

Hello!

First, let's write some important information below:

• Shelby charges $189 for showing up, plus $61 per hour.

,

• Ava charges $153 plus $79 per hour.

• In a determined number of hours, either stylist would cost her the same amount.

Knowing it, let's write it as two equations:

Shelby:

`189+61h`

Ava:

`153+79h`

Remember that in a specific number of hours (h), the cost will be the same. So, we can equal these two equations and find the number h:

`\begin{gathered} 189+61h=153+79h \\ 189-153=79h-61h \\ 36=18h \\ h=(36)/(18) \\ \\ \boxed{h=2} \end{gathered}`

So, the number of hours is 2.

The cost will be $311.

`\begin{gathered} 189+61h=153+79h \\ 189+61(2)=153+79(2) \\ 189+122=153+158 \\ 311=311 \end{gathered}`