The theater sold 82 children tickets and 60 adult tickets.
Step-by-step explanation:
No. of tickets sold = 142
Total sales = $890
Cost of one child ticket = $5
Cost of one adult ticket = $8
Let,
x be the number of children tickets
y be the number of adult tickets
According to given statement;
x+y=142 Â Â Eqn 1
5x+8y=890 Â Eqn 2
Multiplying Eqn 1 by 5
[tex]5(x+y=142)\\5x+5y=710\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+8y)-(5x+5y)=890-710\\5x+8y-5x-5y=180\\3y=180[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{180}{3}\\y=60[/tex]
Putting =60 in Eqn 1
[tex]x+60=142\\x=142-60\\x=82[/tex]
The theater sold 82 children tickets and 60 adult tickets.
Keywords: linear equations, subtraction
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