if the sum of the positive integers x and y is 12 then x can be equal to all of the following except
5y
4y
3y
2y
y
hint: 5y cannot divide 12
To determine which options for x are not possible, we can use algebraic reasoning. We know that the sum of x and y is 12, so we can write this as an equation:
x + y = 12
Now let's substitute the given options for x and see if any of them are not possible.
1. Substituting x = 5y into our equation:
5y + y = 12
Simplifying:
6y = 12
Dividing both sides by 6:
y = 2
Therefore, x = 5y becomes x = 5(2) = 10, which is a possible solution.
2. Substituting x = 4y into our equation:
4y + y = 12
Simplifying:
5y = 12
Dividing both sides by 5:
y = 2.4
Therefore, x = 4y becomes x = 4(2.4) = 9.6, which is not a positive integer. Therefore, x cannot be equal to 4y.
3. Substituting x = 3y into our equation:
3y + y = 12
Simplifying:
4y = 12
Dividing both sides by 4:
y = 3
Therefore, x = 3y becomes x = 3(3) = 9, which is a possible solution.
4. Substituting x = 2y into our equation:
2y + y = 12
Simplifying:
3y = 12
Dividing both sides by 3:
y = 4
Therefore, x = 2y becomes x = 2(4) = 8, which is a possible solution.
5. Substituting x = y into our equation:
y + y = 12
Simplifying:
2y = 12
Dividing both sides by 2:
y = 6
Therefore, x = y becomes x = 6, which is a possible solution.
In conclusion, x cannot be equal to 4y.