The floor of a dance studio is covered with 435 tiles. The owner of the studio replaced the tiles last year. The tiles cost $15 for a set of 8 and $2 for each additional tile.
What is the monthly increase the owner charged each of her 34 students over a 6-month period to cover the cost of replacing the tiles?
To calculate the monthly increase the owner charged each student, we need to first determine the total cost of replacing the tiles.
The owner replaced the tiles in the studio, and the tiles cost $15 for a set of 8. We can start by finding out how many sets of 8 tiles were needed.
Since there are 435 tiles in total, we divide this by 8 to find the number of sets: 435 / 8 = 54.375 sets.
Since we can't have a fraction of a set, we round up the number of sets to the next whole number, which is 55 sets.
Next, we need to calculate the cost of these sets. The first set costs $15, but for each additional tile, the cost is $2. So for the additional 54 sets, we multiply 54 by $2: 54 * $2 = $108.
The total cost of the tiles is $15 for the first set and $108 for the additional sets. Adding these together, we find the total cost to replace the tiles: $15 + $108 = $123.
Now we can calculate the monthly increase for each student. The total cost of the tiles is $123, and the cost should be covered over a 6-month period. So, we divide the total cost by the number of months: $123 / 6 = $20.50.
Therefore, the monthly increase the owner charged each student is $20.50.