SOLUTION: I need help explaining how I know I have the numbers in this word problem in the correct blanks. I already have the blanks filled in, but I don't know how to explain. The movie

Question 903820: I need help explaining how I know I have the numbers in this word problem in the correct blanks.
I already have the blanks filled in, but I don't know how to explain.
The movie theater had 100 people in the audience at the matinee performance. An adult ticket costs $6.00. Tickets for both children under 12 years of age and senior citizens cost $4.00. The theatre took in a total of $450.00 on ticket sales, so the number of adult tickets sold was 25.
The blanks were:
- 100
- $6.00
- $4.00
- $450.00
-25
Thanks a lot! I really appreciate your help :)

Found 2 solutions by richwmiller, josgarithmetic:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
You didn't explain what the blanks were labeled or is that what you are supposed to do
- 100 total tickets
- $6.00 adult ticket price
- $4.00 children and senior
- $450.00 amt received for tickets
-25 adult tickets sold
and you left out 75 for children and seniors
a+c=100,
6*a+4*c=450
a=100-c
6*(100-c)+4*c=450
600-6c+4*c=450
-2*c=-150
c=75
a=100-c
a=25 s at $6 and c=75 at $4
check
25+75=100
6*a+4*c=450
6*25+4*75=450
150+300=450
450=450
ok

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Two types of audience members: Adults and all others. "Adults" will not include Senior Citizens.

x count of adults
y count of all others which is children under 12 and senior citizens combined.

The description gives these equations:
x+y=100, and 6x+4y=450

The system after simplifying the money equation is

Starting with Elimination Method will be easiest; multiply the ticket count equation by 2 and subtract one equation from the other.

.
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