Question

The question attached please.

Answer 1

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;

$5(3a+4c=67)\\15a+20c=335\ \ \ Eqn\ 3$

Multiplying Eqn 2 by 3;

$3(5a+6c=106)\\15a+18c=318\ \ \ Eqn\ 4$

Subtracting Eqn 4 from Eqn 3

$(15a+20c)-(15a+18c)=335-318\\15a+20c-15a-18c=17\\2c=17$

Dividing both sides by 2

$\frac{2c}{2}=\frac{17}{2}\\c=8.5$

Putting c=8.5 in Eqn 1

$3a+4(8.5)=67\\3a+34=67\\3a=67-34\\3a=33$

Dividing both sides by 3;

$\frac{3a}{3}=\frac{33}{3}\\a=11$

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

#LearnwithBrainly