A math teacher wishes to use groups of 5 and/or 7 students for a class assignment. When she tries to make assignments she notices that it cannot be done with the number of students in her class. However, if the number of students were any larger, the assignments could be made. How many students does the teacher have?
35
34
To solve this problem, we need to find the smallest number that cannot be formed by using groups of 5 and/or 7. Let's call this number "x".
To find the value of x, we can use the concept of the Chicken McNugget Theorem. According to this theorem, if two numbers, let's say a and b, are coprime (meaning they have no common factors other than 1), then the largest number that cannot be expressed as a combination of a and b is given by (a * b) - (a + b).
In this case, the numbers 5 and 7 are coprime since their only common factor is 1. So, the smallest number that cannot be formed by using groups of 5 and/or 7 is given by (5 * 7) - (5 + 7), which is equal to 35 - 12 = 23.
Now that we know that the teacher has fewer than 23 students, but would be able to make assignments with any larger number of students, we can conclude that the teacher must have 22 students.