One adult ticket costs £11 and one child ticket costs £8.5
Step-by-step explanation:
Let,
Adult ticket = a
Child ticket = c
According to given statement;
3a+4c=67 Eqn 1
5a+6c=106 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(3a+4c=67)\\15a+20c=335\ \ \ Eqn\ 3[/tex]
Multiplying Eqn 2 by 3;
[tex]3(5a+6c=106)\\15a+18c=318\ \ \ Eqn\ 4[/tex]
Subtracting Eqn 4 from Eqn 3
[tex](15a+20c)-(15a+18c)=335-318\\15a+20c-15a-18c=17\\2c=17\\[/tex]
Dividing both sides by 2
[tex]\frac{2c}{2}=\frac{17}{2}\\c=8.5[/tex]
Putting c=8.5 in Eqn 1
[tex]3a+4(8.5)=67\\3a+34=67\\3a=67-34\\3a=33[/tex]
Dividing both sides by 3;
[tex]\frac{3a}{3}=\frac{33}{3}\\a=11[/tex]
One adult ticket costs £11 and one child ticket costs £8.5
Keywords: Linear equation, subtraction
Learn more about linear equations at:
- brainly.com/question/10666510
- brainly.com/question/10699220
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