P6 Math: Bill shared by 3 people but one of them paid first

A bill is shared equally by 3 people whom have different amounts of money at first.

This is a very unique question that requires students to make use of "Total Unchanged" to visualize the models between all 3 parties.

Such questions usually appear in Paper 2 of P6 exams.
Calculator usage is allowed.

Mary, Roger and Ken shared the cost of a gift for their father equally.
If Mary paid for the gift first, the amount she have remaining will 
be 4/9 of the amount of what Roger have at first. 
If Roger paid first, the amount he have remaining will 
be 11/15 of the amount of what Mary have at first.
If Ken paid first, he'd have no money remaining.

If Roger had $126 more than Mary at first,
how much did the gift cost?


If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 
Copy below question down before making attempt.