Question

34,000 people attended a ballgame at a stadium that offers two kind of seats: general admission and reserved. The day's receipts were $176,000. How many people paid $14.00 for reserved seats, and how many paid $6.00 for general admission?...Show more

Answer 1

The number of people who paid $ 12 for reserved seat is 5,000

The number of people who paid $ 4 for general seat is 29,000

Explanation:

Given as :

The total number of people attending a ballgame = 34,000

The total receipt of the ticket's seat = $ 176,000

The amount pad for reserved seat = $ 12

The amount paid for general admission = $ 4

Let The number of people for reserved seat = r

And The number of people for general admission = g

Now, According to question

The total number of people attending a ballgame = The number of people for reserved seat + The number of people for general admission

or, r + g = 34,000 ...........1

The total receipt of the ticket's seat = The amount pad for reserved seat × The number of people for reserved seat + The amount paid for general admission × The number of people for general admission

Or, $ 12 × r + $ ×4 g = $ 176,000 .........2

or, $ 12 × ( r + g ) = $ 12 × 34000

Or, $ 12 r + $ 12 g = $ 408,000

Solving equation

( $ 12 r + $ 12 g ) - ($ 12 r + $ 4 g ) = $ 408,000 - $ 176,000

Or, ( $ 12 r - $ 12 r ) + ( $ 12 g - $ 4 g ) = $ 232,000

Or 0 + 8 g = 232,000

∴ g =
`(232000)/(8)`

I.e g = 29,000

So , The number of people for general admission = g = 29,000

Put the value of g in Eq 1

I.e r + g = 34,000

or , r = 34,000 - g

∴ r = 34000 - 29000

I.e r = 5,000

So, The number of people for reserved seat = r = 5,000

Hence The number of people who paid $ 12 for reserved seat is 5,000

And The number of people who paid $ 4 for general seat is 29,000 Answer