Question

Suppose you always eat a particular brand of cookies out of the standard sized package it comes in from the store. You notice that when you eat 3 at a time, there's always 1 cookie left over. You decide when you purchase the next package, you'll eat 5 at a time, but still, there's always 1 cookie left over. Since it really isn't helpful to always have a leftover cookie, you decide to eat 7 at a time, and there are no cookies leftover. If you know there are less than 100 cookies in the package, how many cookies are there?

Answer 1

There are 91 cookies in the package of cookies

Explanation:

The given parameter for the number of cookies are;

The number of cookies left when eating 3 at a time = 1 cookie

The number of cookies left when eating 5 at a time = 1 cookie

The number of cookies left when eating 7 cookies at a time = No cookie leftover

Let 'n' represent the number of cookies in the pack, let 'a', 'b', and 'c' be the multiples of 3s, 5s, and 7s in 'n', respectively, we have;

The number of cookies in the pack, n < 100

Therefore, we have;

3·a = n - 1

5·b = n - 1

7·c = n

∴ n - 1 is a multiples of 3 and 5 less than 100 which are;

15, 30, 45, 60, 75, and 90

Therefore, the possible values of 'n' are'

n = n - 1 + 1 = 15 + 1 = 16, 30 + 1 = 31, 45 + 1 = 46, 60 + 1 = 61, 75 + 1 = 75, 90 + 1 = 91

Multiples of 7 includes;

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98

Therefore, n = 91 which is the number that appear simultaneously in both search

The number of cookies in a package = 91 cookies