I need help setting up equation to solve

Question

if hotdog buns come in a package of 9 and all beef franks come in a package of 11, then what's the fewest number of people you could serve a hotdog to and not have any partial packages left over? (serving no people is not considered an option).  99 b) now, suppose that everyone wants relish on their hotdog. if relish comes in packages of 19 servings, what's the fewest number of people you could serve a hotdog with relish to without having any partial packages left over?   c) how many packages of relish would be used serve a hotdog with buns and relish without having any partial packages left over?

Answer 1

Lowest common multiples!

9, 11, and 19 have no common factors, so the LCMs are all just the products of the numbers.)

a) 9 * 11 = 99

b) 9 * 11 * 19 = 1881

c) 1881 / 19 = 99

 

(Also, packages of buns = 11*99 = 1089; packages of franks = 9*19 = 171.)