Adult tickets cost $2.50 more than the children tickets:

let 'x' represent the cost of a children's ticket, then 'x+2.5' represents the cost of an adult's ticket

income from the adult tickets was $50 less than five times the income from the children tickets:

we know that since 150 children's tickets were sold that '150x' represents the income from children's tickets, so '5(150x)-50' represents the income from adult tickets

400 adult tickets and 150 children tickets were sold, so we set the income per ticket equal to the total revenue per ticket type:

400(x+2.5) + 150x = 150x + (5(150x)-50)

solving for 'x' we have:

x=3

3+2.5=5.5

The cost of a child's ticket is $3.00, the cost of an adult's ticket is $5.50