Answer to Question #253873 in Combinatorics | Number Theory for Guen

Question

lan's Cafà ƒ © and Restaurant is offering a promo. They charge PHP 250 per person for a group of five. If the group has more than five persons, the first five persons pay the same and the rest shall pay PHP 100 each. A group of more than five people decided to divide the bill equally amongst themselves. How many people were in the group if each of them paid PHP 130?

Answer 1

$130x=250\cdot5+100y$

where x number of persons in group,

y is number of persons who is not in first five persons.

$13x-10y=125$

minimal values:

$x=15,y=7$

Answer: 15 people in the group.