Let's break down the information given and analyze the cost structure of each gym to formulate the system of equations.
We are given that "Fit Fast" charges a set fee per class, and "Stepping Up" charges a monthly fee in addition to a fee per class.
First, let's define a few variables:
- Let [tex]\( y \)[/tex] be the total cost.
- Let [tex]\( x \)[/tex] be the number of fitness classes Anna takes.
### Fit Fast Gym:
Fit Fast charges a set fee per class. This means the total cost for this gym is simply the fee per class multiplied by the number of classes. We are given:
[tex]\[ y = 5.5x \][/tex]
### Stepping Up Gym:
Stepping Up charges a monthly fee plus an additional fee per class. This fee structure combines a fixed fee (monthly fee) with a variable fee dependent on the number of classes. We are given:
[tex]\[ y = 7.5x + 10 \][/tex]
### System of Equations:
To find the system of equations representing these costs, we set up the equations described above:
For Fit Fast:
[tex]\[ y = 5.5x \][/tex]
For Stepping Up:
[tex]\[ y = 7.5x + 10 \][/tex]
### Conclusion:
The system of equations representing the costs of the two gyms is:
1. [tex]\( y = 5.5x \)[/tex]
2. [tex]\( y = 7.5x + 10 \)[/tex]
Thus, the correct choice from the given options is:
[tex]\[ y=7.5 x \text{ and } y=5.5 x+10 \][/tex]
