Answer:
15 children and 5 adults
Step-by-step explanation:
Lets call the adults 'a' and the children 'c'.
We know that 20 tickets by a family was purchased so a + c = 20.
We also know that the total cost of the tickets was $100 and one adult ticket cost $8 and one child cost $4 so 8a + 4c = 100
Now we have simultaneous equations,
α) a + c = 20
β) 8a + 4c = 100
→ Multiply α) by 8 to make the same 'a' coefficient
α) 8a + 8c = 160
β) 8a + 4c = 100
→ Minus the α) from β)
4c = 60
→ Divide both sides by 4 to work out how many child tickets were bought
c = 15
→ Substitute the value of c = 15 back into the equation of a + c = 20
a + 15 = 20
→ Minus 15 from both sides to work out how many adult tickets were bought
a = 5
