You and your friends form a band. You want to record a demo. Studio A rents for $100 up front plus $50 per hour. Studio B rents for $50 up front plus $75 per hour. After how many hours will the rent be the same? What will the rent be? .......... PLEASE HELP. I NEED THIS TO BE SOLVED WITH SUBSTITUTION AND CANNOT UNDERSTAND.
let the number of hours be h
costA = 100 + 50h
costB = 50 + 75h
they are the same when costA = costB
100 + 50h = 50 + 75h
50 = 25h
h = 2
when h = 2, costA = costB = 50+75(2) = 200
(could use either equation, since they are equal)
To solve this problem using substitution, let's start by assigning variables to the unknown quantities:
Let's say the number of hours spent in both studios is represented by 'x', and the total cost for renting Studio A is represented by 'y'.
For Studio A:
Upfront cost = $100
Cost per hour = $50
For Studio B:
Upfront cost = $50
Cost per hour = $75
The equation for the total cost for Studio A can be expressed as:
y = 100 + 50x
The equation for the total cost for Studio B can be expressed as:
y = 50 + 75x
To find when the rent will be the same, we need to set the two equations equal to each other and solve for x:
100 + 50x = 50 + 75x
Now, let's solve this equation step by step:
Subtract 50x from both sides:
100 = 50 + 25x
Subtract 50 from both sides:
50 = 25x
Divide both sides by 25:
2 = x
So, after 2 hours, the cost of renting Studio A and Studio B will be the same.
To find the cost, we can substitute this value of 'x' into either of the original equations. Let's use the equation for Studio A:
y = 100 + 50x
y = 100 + 50(2)
y = 100 + 100
y = 200
Therefore, after 2 hours, the rent will be the same, and the cost will be $200 for both studios.