Question

5 adult tickets and 3 child tickets to a concert costs £99. 8 adult tickets and 6 child tickets costs £168. How much do adult and child tickets cost?

Answer 1

Explanation:

Let's denote the cost of an adult ticket by 'a' and the cost of a child ticket by 'c'. We can set up a system of two equations based on the given information:

Equation 1: 5a + 3c = 99

Equation 2: 8a + 6c = 168

We can solve for 'a' and 'c' by using elimination or substitution. Here, we'll use elimination:

Multiplying Equation 1 by 2, we get:

10a + 6c = 198

Subtracting Equation 2 from this, we get:

(10a + 6c) - (8a + 6c) = 198 - 168

Simplifying, we get:

2a = 30

Dividing both sides by 2, we get:

a = 15

Substituting this value of 'a' into Equation 1, we get:

5(15) + 3c = 99

Simplifying, we get:

75 + 3c = 99

Subtracting 75 from both sides, we get:

3c = 24

Dividing both sides by 3, we get:

c = 8

Therefore, an adult ticket costs £15 and a child ticket costs £8.