SOLUTION: admission prices for a football game were $6 for adults and $2 dollars for children the total value of tickets sold was $2528 and 454 tickets were sold. how many adults and childre

Question 620173: admission prices for a football game were $6 for adults and $2 dollars for children the total value of tickets sold was $2528 and 454 tickets were sold. how many adults and children attended the game?
Found 2 solutions by solver91311, dragonwalker:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Solve the system for where will represent the number of adult tickets sold and will represent the number of children's tickets sold. You can't actually tell how many adults and children attended the game since you have no guarantee that the act of purchasing a ticket resulted in the attendance of an individual at the game in every case.

John

My calculator said it, I believe it, that settles it

Answer by dragonwalker(73) (Show Source): You can put this solution on YOUR website!
You need to find the mean cost of a ticket:
2528/454 = $5.568
You want to know how many children's tickets were bought for each single adult ticket to give such a mean, so let us say that for every one adult ticket at $6 't' children's tickets were bought at $2.
To find the mean we add these together and divide by the number (t + 1) (i.e. number of children's tickets to every one adult plus the one adult ticket). This formula will equal the mean cost so:
2t + 6/(t+1) = 5.568
solve for t:
2t + 6 = 5.568 (t+1)
2t + 6 = 5.568t + 5.568
6 - 5.568 = 5.568t - 2t
0.432 = 3.568t
t = 0.432/3.568
t = 0.121
so for every adult ticket, 0.121 children's tickets were sold. So now we need to find how many of each were sold.
So let us call the total number of adult tickets 'T' so 0.121T children's tickets are sold. Which would equal the total number 454
So:
T + 0.121T = 454
1.121T = 454
T = 454/1.121
T = 405
so 405 adult tickets were sold and therefore 405 x 0.121 = 49 children's tickets.
To check multiply the number of tickets by their respective costs and add together:
(405x6) + (49x2) = 2430 + 98
=$2528 !!!
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