Answer:
There are 91 cookies in the package of cookies
Step-by-step 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
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