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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Evan wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Evan can pay per month, plus for each group class he attends. Alternately, he can get the second membership plan and pay per month plus per class. If Evan attends a certain number of classes in a month, the two membership plans end up costing the same total amount. What is that total amount? How many classes per month is that?Each membership plan costs if Evan takes classes per month.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Evan wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Evan can pay per month, plus for each group class he attends. Alternately, he can get the second membership plan and pay per month plus per class. If Evan attends a certain number of classes in a month, the two membership plans end up costing the same total amount. What is that total amount? How many classes per month is that?Each membership plan costs if Evan takes classes per month.
- Define Variables: Let's define the variables:Let be the number of classes Evan attends per month.Let be the total cost for each membership plan when they are equal.Now, we can write the equations for each membership plan based on the given information:First membership plan: per month + per classSecond membership plan: per month + per classThe equations representing the total cost for each plan are:First membership plan: Second membership plan: Since the total cost is the same for both plans, we can set the equations equal to each other:
- Write Equations: Now, we will solve for by isolating the variable:Subtract from both sides:Subtract from both sides:Divide both sides by :So, Evan attends classes per month.
- Solve for x: Now that we know Evan attends classes per month, we can find the total cost for each membership plan.Using the first membership plan's equation:So, the total cost for each membership plan is when Evan takes classes per month.
