Question

Dapper Dan's Dancing School charges $85 for enrollment plus $6 per class, whereas Leaping Larry's Dancing School charges $40 for

enrollment plus $12 per class. For how many classes will Leaping Larry's Dancing School be more expensive?

A:Seven or fewer classes
B:Seven or more classes
C:Eight or fewer classes
D:Eight or more classes

Answer 1

D

Explanation:

Let D represent the total cost for attending x lessons for Dan’s Dancing School and let L represent the total cost for attending x lessons for Larry’s Dancing School.

Dan’s Dancing School charges $85 for enrollment plus $6 per class. So, we can write the following equation:

`D=6x+85`

Larry’s Dancing School charges $40 for enrollment and $12 per class. So, we can write the following equation:

`L=12x+40`

Let’s find the value of x such that the cost will be the same. So, set the equations equal to each other and solve for x:

`6x+85=12x+40`

Subtract 6x from both sides:

`85=6x+40`

Subtract 40 from both sides:

`45=6x`

Divide both sides by 6:

`x=7.5`

Since we can’t have half a class, we need to round up to the nearest whole number.

However, notice that Larry’s class charges more per class than Dan’s. Therefore, for any number after 7.5, Larry’s class will be more expensive.

Since we can’t have 7.5 classes, we are rounding it to 8.

Therefore, after 8 or more classes, Larry’s class will be more expensive.

So, our correct answer is D.