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Tcecarenko [31]
2 years ago
14

The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive l

arge 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? ____________
Mathematics
1 answer:
Nezavi [6.7K]2 years ago
8 0

- Make an equation representing the number of vehicles needed.

We have six drivers so

x + y ≤ 6

That's not really an equation; it's an inequality.  We want to use all our drivers so we can use the small vans, so

x + y = 6

- Make an equation representing the total number of seats in vehicles for the orchestra members.

s = 25x + 12y

That's how many seats total; it has to be at least 111 so again an inequality,

25x + 12y ≥ 111

We solve it like a system of equations.  

x + y = 6

y = 6 - x

111 = 25x + 12y = 25x + 12(6-x)

111 = 25x + 72 - 12x

111 - 72 = 13 x

39 = 13 x

x = 3

Look at that,  it worked out exactly.  It didn't have to.

y = 6 - x = 3

Answer: 3 buses, 3 vans

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