Two friends from a band want to record a demo. Studio A rents for a fee of $110 plus $50 an hour. Studio B rents for $190 fee fplus $40 an hour. What is the difference in renting Studio A for n hours rather than Studio B? How many hours would they have to rent so the cost of renting Studio A is the same as renting Studio B?
To find the difference in renting Studio A for n hours rather than Studio B, we need to calculate the total cost for both studios and find the difference between them.
The total cost of renting Studio A for n hours can be calculated by adding the base fee to the cost per hour multiplied by the number of hours:
Total cost of Studio A = $110 + ($50 * n)
Similarly, the total cost of renting Studio B for n hours can be calculated using the same formula:
Total cost of Studio B = $190 + ($40 * n)
Now, to find the difference in renting Studio A for n hours rather than Studio B, we subtract the total cost of Studio B from the total cost of Studio A:
Difference = (Total cost of Studio A) - (Total cost of Studio B)
Difference = [$110 + ($50 * n)] - [$190 + ($40 * n)]
Difference = $110 + ($50 * n) - $190 - ($40 * n)
Difference = $110 - $190 + ($50 * n - $40 * n)
Difference = $-80 + $10 * n
So, the difference in renting Studio A for n hours rather than Studio B is $-80 + $10 * n.
Now, let's find the number of hours they would have to rent so the cost of renting Studio A is the same as renting Studio B. We can set up an equation to represent this situation:
Total cost of Studio A = Total cost of Studio B
$110 + ($50 * n) = $190 + ($40 * n)
To solve for n, we need to isolate the variable:
$50 * n - $40 * n = $190 - $110
$10 * n = $80
Dividing both sides by $10:
n = $80 / $10
n = 8
Therefore, they would have to rent Studio A for 8 hours so the cost is the same as renting Studio B.