To determine which plan would be less expensive based on the number of visits Raul makes to the gym, we can use a comparison of linear models.
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Set price per visit: This can be represented as \( y = mx \), where \( m \) is the cost per visit and \( x \) is the number of visits. There is no fixed fee here, so the line will start at the origin (0,0).
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Membership plan: This can be expressed with the equation \( y = mx + b \), where \( m \) is the lower cost per visit with a membership, \( b \) is the membership fee, and \( x \) is the number of visits. This line will start above the origin (at the point where \( y = b \) when \( x = 0 \)).
To find the point at which both costs are the same, you can set the equations equal to each other if you want to compare to find the break-even point.
- The two equations are:
- Pay per visit: \( y = mx \)
- Membership plan: \( y = nx + b \)
You would solve the equation \( mx = nx + b \) for \( x \) to find out at what number of visits the costs are equal.
In summary, the model used to determine which plan is less expensive will involve comparing two linear equations, and specifically finding their intersection or analyzing their slopes to determine which option is better based on the number of visits. The graphical representation would show two lines where you could easily see which line is below the other for specific ranges of visits.
If you have specific graphs options labeled as MAMAT080810272_Aa.gif, MAMAT080810272_Ba.gif, MAMAT080810272_Ca.gif, and MAMAT080810272_Da.gif, you would look for the one that shows two lines (one starting at the origin and one starting higher) to represent these two plans. Please provide those images or more details for a more specific selection.
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