Answer:
Step-by-step explanation:
Studio A rents for $75 plus $75 an hour .
Studio B rents for $150 and $50 an hour.
Let t = the number of hours and c = cost.
Part A
Write a system of equations to represent the cost at each studio.
Studio A: c = 75 +75·t
Studio B: c = 150 +50·t
Part B
Solve the system of equations from Part A. Explain your method.
We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.
150 +50·t = 75 +75·t, subtract 75 and 50t from both sides
150 -75 = 75t -50t, combine likes terms
75 = 25t, divide both sides by 25
3 = t
Now we know that t = 3 so we find c by substituting t with 3 in the second equation.
c = 150 +50·t
c = 150 +50·3
c = 300
The solution of the system of equations is c = 300 and t = 3
Part C
Explain what the solution to the system means in terms of where your band will rent a studio.
The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.
The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.
.