SOLUTION: 1000 people at concert. X were adults and y were kids. Adults cost 10 Euro and kids cost 5 Euro. Total amount 8750 Euro. How many were kids and how many were adults

Question 1101700: 1000 people at concert. X were adults and y were kids. Adults cost 10 Euro and kids cost 5 Euro. Total amount 8750 Euro. How many were kids and how many were adults
Found 4 solutions by Shin123, richwmiller, josgarithmetic, greenestamps:
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
750, 250
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
"tutor" Shin123
From the owner and webmaster:
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My take on the alligation method.
8750 euro = 1000 tickets at 8.75 euro each
Let A denote the 10 Euro tickets and B denote the 5 Euro tickets which we have.
Let C denote the 8.75 Euro which we want.
Using the method of alligation.

10 3.75 3.75/5.0*1000=750 adults at 10 Euro 8.75 750+250= 1000 tickets of 8.75 Euro 5 1.25 1.25/5.0*1000=250 Kids at 5 Euro 5.0

1.25= 10 - 8.75
3.75= 8.75 - 5
E.g. There are 3.75 parts of A plus 1.25 parts of B
Then 3.75+1.25=5.0 parts total
3.75/5.0=0.75
0.75*1000=750
750 adult at 10 euro
1000 tickets-750 adult=250 kids
250.0 kids of 5 euro
or
1.25/5.0=0.25
0.25*1000=250 Euro
250.0 kids at 5 euro.
check
0.05 * 250 + 0.1 * 750 = 0.0875*1000
12.5 + 75.0 = 87.5
87.5 = 87.5
ok
Thank you greenestampes for introducing me to alligation.
Answer by josgarithmetic(39631)   (Show Source): You can put this solution on YOUR website!
(Adjusted Problem Statement)
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1000 people at concert. x were adults and y were kids. Adults price 10 Euro and kids price 5 Euro. Total sales revenue was 8750 Euros. How many were kids and how many were adults?
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The description literally is this system of equations:

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Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

This is really a "mixture" word problem: you are mixing 5 euro tickets and 10 euro tickets and coming out with an average ticket price of 8750/1000 = 8.75 euros.

By far the easiest way to solve a problem like this is with the method of alligation. Do an internet search on "alligation" if you are interested in learning more about it.

Here is my version of alligation, used to solve this problem quickly and easily.

The lower ticket price is 5; the average ticket price is 8.75; the higher ticket price is 10.

Where does the 8.75 lie "on a number line" between 5 and 10? It is 3/4 of the way from 5 to 10. (8.75-5 = 3.75; 10-5 = 5; 3.75/5 = 3/4).

That means that 3/4 of the tickets must be the higher price.

So 1/4 of the 1000 tickets (250) are 5 euro tickets, and 3/4 of the 1000 (750) are 10 euro tickets.
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