for a production of sweeney Todd in Las Vegas, orchestra seats cost $42 and mezzanine seats cost $25. if a group of 14 people show up and spend a total of $486, how many of each kind of seat did they buy? use elimination to solve. please help!
Accepted Solution
A:
They buy 8 orchestra seats and 6 mezzanine seatsStep-by-step explanation:For a production of Sweeney Todd in Las VegasOrchestra seats cost $42Mezzanine seats cost $25A group of 14 people show up and spend a total of $486We need to find how many of each kind of seat they boughtAssume that the group of people takes x orchestra seats and y mezzanine seats∵ The group of 14 people show up∵ x represents the number of orchestra seats∵ y represents the number of mezzanine seats∴ x + y = 14 ⇒ (1)∵ Orchestra seats cost $42 each∵ Mezzanine seats cost $25 each∵ The group of people spend a total of $486∴ 42 x + 25 y = 486 ⇒ (2)Now we have system of equations to solve itMultiply equation (1) by -25 to eliminate y∵ -25 x - 25 y = -350 ⇒ (3)- Add equations (2) and (3)∴ 17 x = 136- Divide both sides by 17∴ x = 8Substitute the value of x in equation (1) to find y∵ 8 + y = 14- Subtract 8 from both sides∴ y = 6They buy 8 orchestra seats and 6 mezzanine seatsLearn more:You can learn more about the system of equations in brainly.com/question/2115716#LearnwithBrainly