The cost of adult ticket is $7 and child ticket is $4.
Step-by-step explanation:
Let,
Price of one adult ticket = x
Price of one child ticket = y
According to given statement;
2x+7y=42 Eqn 1
3x+11y=65 Eqn 2
Multiplying Eqn 1 by 3
[tex]3(2x+7y=42)\\6x+21y=126\ \ \ Eqn\ 3[/tex]
Multiplying Eqn 2 by 2
[tex]2(3x+11y=65)\\6x+22y=130\ \ \ Eqn\ 4[/tex]
Subtracting Eqn 3 from Eqn 4
[tex](6x+22y)-(6x+21y)=130-126\\6x+22y-6x-21y=4\\y=4[/tex]
Putting y=4 in Eqn 1
[tex]2x+7(4)=42\\2x+28=42\\2x=42-28\\2x=14\\[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{14}{2}\\x=7[/tex]
The cost of adult ticket is $7 and child ticket is $4.
Keywords: linear equation, elimination method
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