Question 1202593: If 125 people attend a concert and tickets for adults cost $4.00 while tickets for children cost $1.75 and total receipts for the concert was $324.50, how many of each went to the concert?
There were adults and children that attended the concert.
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
Formally....
x = adults
125-x = children
The total cost of the tickets, at $4 per adult and $1.75 per child, was $324.50:
4(x)+1.75(125-x) = 324.50
You can do the work to find the answer. (The algebra is basic, but the numbers are a bit ugly....)
Informally, using logical reasoning and simple arithmetic....
If all 125 tickets were adult tickets, the total cost would have been 125($4) = $500.
The actual total was $324.50, which is $175.50 less than $500.
The difference in the cost of an adult ticket and a child ticket is $4-$1.75 = $2.25.
The number of child tickets, to make the difference of $175.50, was 175.50/2.25 = 702/9 = 78.
ANSWER: 78 children's tickets and 125-78 = 47 adult tickets
CHECK: 78($1.75)+47($4) = 136.50+188 = 324.50
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