CLASS SOLD 82 TICKETS TO CONCERT AND MADE #431. $8 FOR ADULT AND $3 FOR CHILDREN TICKETS. HOW MANY OF EACH WERE SOLD?
adults --- x
children -- 82-x
8x + 3(82-x) = 431
take over from here.
I DON'T KNOW ??? HELP
To find the number of adult and children tickets sold, we can set up a system of equations. Let's define the following variables:
A: Number of adult tickets sold
C: Number of children tickets sold
Based on the information given in the question, we can establish two equations:
1) The total number of tickets sold: A + C = 82
2) The total revenue generated from the ticket sales: 8A + 3C = 431
Now, we can solve this system of equations to find the values of A and C.
Method 1: Substitution
Let's solve for A in the first equation: A = 82 - C
Now, substitute the value of A in the second equation:
8(82 - C) + 3C = 431
656 - 8C + 3C = 431
-5C = -225
C = 45
Substituting the value of C back into the first equation:
A + 45 = 82
A = 82 - 45
A = 37
Therefore, 37 adult tickets and 45 children tickets were sold.
Method 2: Elimination
Multiply the first equation by 3 to eliminate the variable C:
3A + 3C = 246
Subtract this equation from the second equation:
(8A + 3C) - (3A + 3C) = 431 - 246
5A = 185
A = 37
Substituting the value of A back into the first equation:
37 + C = 82
C = 82 - 37
C = 45
Therefore, 37 adult tickets and 45 children tickets were sold.
Both methods yield the same answer: 37 adult tickets and 45 children tickets were sold.