Question

At Joe's Grocery, you can buy hot dogs only in packages of 4 or packages of 7. As a result, you can't buy exactly 9 hot dogs since it is not possible to combine packages of 4 and 7 to get exactly 9 hot dogs. What's the largest possible number of hot dogs that you can't get exactly by buying these hot dog packages at Joe's?

Answer 1

29

Explanation:

Hot Dog packages

4 = 2 *2

7 = 1 * 7

To determine, the largest possible number of hot dogs that you can't get exactly by buying these hot dogs is to determine the LCM ( lowest common multiple of 4 and 7 ) and add 1 to it

LCM of 4 and 7 = 1 * 2 * 2 * 7 = 28

Highest number that combining 7 and 4 packages can't give = 28 + 1 = 29