SOLUTION: There are 640 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1220. How many adults and how many children attended?

Question 182533: There are 640 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1220. How many adults and how many children attended?
Found 2 solutions by Mathtut, eperette:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
There are 640 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1220. How many adults and how many children attended?
:
lets call the number of adults and children, a and c , respectively
:
a+c=640.............eq 1
3a+1c=1220..........eq 2
:
rewrite eq 1 to ....and plug that value into eq 2
:
3(640-c)+c=1220
:
1920-3c+c=1220
:
-2c=-700
:
number of children who attended play
:
number of adults who attended play
Answer by eperette(173) (Show Source): You can put this solution on YOUR website!
Let
a = number of adults
c = number of children
Then
a + c = 640
3a + 1c = 1220
We will solve using elimination (subtraction method)
-1(a + c = 640)
**************
-a - c = -640
3a + c = 1220
**************
2a + 0 = 580
2a/2 = 580/2
a = 290
Now lets go back and substitute a to find c
a + c =640
290+c =640
290-290+c=640-290
0 + c = 350
c = 350
*******************
There were 290 adults and 350 children
CHECK
290+350=640 admissions
290($3) + 350($1)=$870 + $350 = $1,220
answer is right
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