Tickets for a cinema cost £a for adults and £c for children. 2 adults and 3 children cost £42.70. 3 adults and 5 children cost £67.30.

How much does it cost for 1 adult and 1 child?

c = 6.5, a = 11.6

Step-by-step explanation:

2a + 3c = 42.7

3a + 5c = 67.3

Elimination

(2a+3c = 42.7) * 3

(3a+5c = 67.3) * 2

(1) 6a+9c = 128.1

(2) 6a+10c = 134.6

(2) - (1)

c = 6.5

Substitue 'c' in any of the equation

2a + 3 (6.5) = 42.7 or 3a + 5 (6.5) = 67.3

2a + 19.5 = 42.7 3a + 32.5 = 67.3

2a = 42.7 - 19.5 3a = 67.3 - 32.5

2a = 23.2 3a = 34.8

a = 11.6 a = 11.6