The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. make a system of equations to find the smallest number of busses the orchestra can rent. Let x= the number of busses and y= the number of vans make an equation representing the number of vehicles needed. __________ make an equation representing the total number of seats in vehicles for the orchestra members. __________ Solve the system of equations. How many busses does the orchestra need to rent? ____________ How many 12-passenger vans does the orchestra need to rent? ____________

- Make an equation representing the number of vehicles needed.We have six drivers sox + y ≤ 6That's not really an equation; it's an inequality.  We want to use all our drivers so we can use the small vans, sox + y = 6- Make an equation representing the total number of seats in vehicles for the orchestra members.s = 25x + 12yThat's how many seats total; it has to be at least 111 so again an inequality,25x + 12y ≥ 111We solve it like a system of equations.  x + y = 6y = 6 - x111 = 25x + 12y = 25x + 12(6-x)111 = 25x + 72 - 12x111 - 72 = 13 x39 = 13 xx = 3Look at that,  it worked out exactly.  It didn't have to.y = 6 - x = 3Answer: 3 buses, 3 vans