To find out how many classes Gina needs to take for the total cost to be the same at both Dance World and Toe Tappers, we need to solve the system of equations given:
1. Dance World: [tex]\( y = 15x \)[/tex]
2. Toe Tappers: [tex]\( y = 25 + 12.5x \)[/tex]
where [tex]\( y \)[/tex] represents the total cost and [tex]\( x \)[/tex] represents the number of classes.
Step-by-Step Solution:
1. Set the two equations equal to each other to find the number of classes ([tex]\( x \)[/tex]) where the costs are the same:
[tex]\[
15x = 25 + 12.5x
\][/tex]
2. Isolate the variable [tex]\( x \)[/tex] by subtracting [tex]\( 12.5x \)[/tex] from both sides of the equation:
[tex]\[
15x - 12.5x = 25
\][/tex]
3. Simplify the equation:
[tex]\[
2.5x = 25
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 2.5:
[tex]\[
x = \frac{25}{2.5} = 10
\][/tex]
Thus, Gina would need to take 10 classes for the total cost to be the same at both Dance World and Toe Tappers.
