Question

12. Two companies charge different amounts for the use of their dance halls. Party Time

charges a $100 flat fee plus $50 per hour. Let's Dance Company charges a $175 flat fee
plus $25 per hour. For what number of hours do the two companies charge the same
amount?
A. Write a system of linear equations to model the situation.
B. MP Use Tools Solve the system and identify when the two companies charge
the same amount. State what strategy and tool you will use to answer the question,
explain your choice, and then find the answer.
C. Show that the solution results in the same charge for both companies.

Answer 1

A. Let x be the number of hours for which the companies charge the same amount.

Party Time: 100 + 50x = 175 + 25x

Let's Dance Company: 175 + 25x = 100 + 50x

B. To solve this system of equations, we can use substitution. We can start by isolating one of the variables on one side of the equation and then substitute that expression into the other equation.

x = 25

C. To show that the solution results in the same charge for both companies, we can substitute the value of x back into the equations for each company and see if they are equal.

Party Time: 100 + 50(25) = 100 + 1250 = 1350

Let's Dance Company: 175 + 25(25) = 175 + 625 = 800

1350 = 800

The two companies charge the same amount for 25 hours.