There are 49,000 seats in a sports stadium. Tickets for the seats in the upper level sell for $25, the ones in the middle level cost $30 and the ones in the lower level are $35 each. The number of seats in the middle and bottom levels together equal the number of seats in the upper level. When all of the seats are sold for an event, the total revenue is $1,419,500. How many seats have been sold in the upper level?

Question

Mathematics

Urijah Kaufman

1 June, 20:44

There are 49,000 seats in a sports stadium. Tickets for the seats in the upper level sell for $25, the ones in the middle level cost $30 and the ones in the lower level are $35 each. The number of seats in the middle and bottom levels together equal the number of seats in the upper level. When all of the seats are sold for an event, the total revenue is $1,419,500. How many seats have been sold in the upper level?

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Gwendolen · Answer 1

U - amount of upper level tickets which cost 25$

m-amount of middle level tickets which cost 30$

b-amount of bottom level tickets which cost 35$

m+b=u and

m+b+u=49000 and

25u+30m+35b=1419500

putting u from first equation to the second

2u=49000

u=24500 - seats in upper level

m+b=24500 so m=24500-b

25*24500+30 (24500-b) + 35b=1419500

612500+735000-30b+35b=1419500

1347500+5b=1419500

5b=72000 / : 5

b=14400 amount of seads in bottom level