Dance lessons are offered at two studios. The cost of dance lessons at each studio is shown.
• Studio Q charges a $30 registration fee plus $80 per month.
• Studio R charges a $105 registration fee plus $65 per month.
After how many months will the total cost of the dance lessons be equal at the two studios?
5
280
9
430
Let's represent the total cost of dance lessons at Studio Q after x months as Q(x) and the total cost of dance lessons at Studio R after x months as R(x).
We know that Q(x) = 30 + 80x (registration fee plus monthly fee) and R(x) = 105 + 65x.
We want to find the number of months x where Q(x) = R(x).
Setting up the equation:
30 + 80x = 105 + 65x
Simplifying the equation:
80x - 65x = 105 - 30
15x = 75
x = 75/15
x = 5
Therefore, after 5 months, the total cost of dance lessons will be equal at both Studio Q and Studio R.