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Reggie just became a personal trainer and is finalizing his pricing plans. One plan is to charge $\$30$ for the initial consultation and then $\$35$ per session. Another plan is to charge $\$40$ for the consultation and $\$30$ per session. Reggie realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that? $\newline$ Write a system of equations, graph them, and type the solution. $\newline$ $\_\_\_\_$ sessions $\newline$

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Experimental probability

Full solution

Q. Reggie just became a personal trainer and is finalizing his pricing plans. One plan is to charge

\$30

for the initial consultation and then

\$35

per session. Another plan is to charge

\$40

for the consultation and

\$30

per session. Reggie realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that?

\newline

Write a system of equations, graph them, and type the solution.

\newline

\_\_\_\_

sessions

\newline

Define Total Cost: Let's define the total cost for each plan based on the number of sessions, $x$ . For the first plan, the cost is $\$30$ for the consultation plus $\$35$ per session. So, the equation is $30 + 35x$ . For the second plan, it's $\$40$ for the consultation plus $\$30$ per session, giving us the equation $40 + 30x$ .
Set Equations Equal: Now, we set the equations equal to each other to find when the costs are the same: $30 + 35x = 40 + 30x$ .
Subtract and Simplify: Subtract $30x$ from both sides to get $35x - 30x = 40 - 30$ , simplifying to $5x = 10$ .
Divide and Solve: Divide both sides by $5$ to solve for $x$ : $x = \frac{10}{5}$ , which simplifies to $x = 2$ .

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