as president of the student council, brenna needs to decide between two venues for the homecoming dance…

as president of the student council, brenna needs to decide between two venues for the homecoming dance. city ballroom charges a $300 setup fee plus $240 per hour, which includes the services of a dj. la rosa loft doesnt charge a setup fee, but the space costs $295 per hour and does not include a dj. if brenna chooses la rosa loft, she would need to hire an outside dj that costs an additional $45 per hour. how long would the dance need to last for the cost to be the same at either venue? simplify any fractions. hours

as president of the student council, brenna needs to decide between two venues for the homecoming dance. city ballroom charges a $300 setup fee plus $240 per hour, which includes the services of a dj. la rosa loft doesnt charge a setup fee, but the space costs $295 per hour and does not include a dj. if brenna chooses la rosa loft, she would need to hire an outside dj that costs an additional $45 per hour. how long would the dance need to last for the cost to be the same at either venue? simplify any fractions. hours

Answer

Explanation:

Step1: Set up cost equations

Let ( x ) be the number of hours. For City Ballroom: ( C_1 = 300+240x ) For La Rosa Loft: ( C_2=(295 + 45)x=340x )

Step2: Set ( C_1 = C_2 ) and solve for ( x )

[ \begin{align*} 300+240x&=340x\ 300&=340x - 240x\ 300&=100x\ x&=\frac{300}{100}\ x& = 3 \end{align*} ]

Answer:

( 3 )