2 family go to the thetre the smiths family of 3 adults and 4 children pay £67 the jones family of 5 adults and 6 children pay £106 work out the cost of an adult and child ticket

The answer to your question is:

adult = £ 11

children = £ 8.5

Step-by-step explanation:

Data

Smiths 3 adults 4 children £67

Jones 5 adults 6 children £ 106

adult = a

child = c

Process

3a + 4c = 67 (1)

5a + 6c = 106 (2)

Solve the equations using the elimination method

Multiply (1) by - 5 - 15a - 20c = - 335

Multiply (2) by 3 15a + 18c = 318

0 - 2c = - 17

c = 17/2

c = £ 8.5

Solve (1) for a 3a + 4 (17/2) = 67

3a + 34 = 67

3a = 67 - 34

3a = 33

a = 33/3

a = £11