Integer Constraints
ex. If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates? (54, 55, 56, 57, 58)
If Kelly received 1/3 more votes than Mike, she received 4/3 the number of votes. So what times 4/3 will equal an integer? only multiple of 3 will cancel out the 3 in the denominator. the number of votes Mike received is a multiple of 3, then the number of votes Kelly received must be a multiple of 4. Taken together, the total number of votes cast must then be a multiple of 7. (answer is 56)