Q:

music band came to town. The amphitheater filled all 50,000 seats at two-level pricing. Level 1 tickets are $150 each, and level 2 tickets are $250 each. The amphitheater made $125,000 in ticket sales. The system of equations that models this scenario is: x + y = 50,000 150x + 250y = 125,000 What do the x and y represent in the system?

Accepted Solution

A:
In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats. Given to us,system of equations,Equation 1, 150x + 250y = 125,000,Equation 2,  x + y = 50,000,Total number of seats = 50,000 seats,Total number of sales = $125,000,Level 1 tickets price = $150,Level 2 tickets price = $250,Let us assume, Number of tickets of Level 1 is [tex]\bold x[/tex], and, Number of tickets of Level 2 is [tex]\bold y[/tex],Total sales = (Number of tickets of Level 1 x Level 1 tickets price ) + (Number of  tickets of Level 2 x Level 2 tickets price )125,000 = ([tex]\bold x[/tex] x 150) + ([tex]\bold y[/tex] x 250)125,000 = 150x + 250yNow,Total number of seats = Number of tickets of Level 1 + Number of tickets of Level 250,000 = x + yTherefore, In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats. To know more visit: