4 adults + 5 children = 259
12 adults + 15 children = 777

3 adults + 6 children = 246
12 adults + 24 children = 984

24-15 children = 984 - 777
9 children = 207
1 child = $23

admission cost for 1 child is $23


...

Alternative method

$259 for 4 adult and 5 children tickets
$246 for 3 adult tickets and 6 children tickets


Notice that there are 9 people for both cases. Both cases have 5 children and 3 adults tickets in common.

So difference between the price for the two cases is just the difference between 1 child and 1 adult ticket.

Difference = $259 - $246 = $13

So 1 adult ticket cost $13 more than 1 child ticket.


Change the adult tickets to children tickets by subtracting $13 from each case.


$259 for 4 adult 5 children :

Convert the 4 adult tickets,
$259 - $13 x 4 = $259 - $52 = $207

So $208 is the cost of 9 child tickets.

1 child ticket = $207 ÷ 9 = $23


Or


$246 for 3 adults 6 children

Convert the 3 adult tickets,
$246 - $13 x 3 = $246 - $39 = $207

Same as above,
$207 is the cost of 9 child tickets.

1 child ticket = $207 ÷ 9 = $23