If the sum of the positive integer a and 5 is less than 12, what is the sum of all possible values of a?
5 + a <12
a = 6
a = 5
a = 4
a = 3
a = 2
a = 1
a = 0
and many negative numbers
The sum of the positive integer a and 5 is less than 12, which can be represented as:
a + 5 < 12
To find all possible values of a, we subtract 5 from both sides of the inequality:
a < 12 - 5
This simplifies to:
a < 7
Therefore, all possible values of a are integers less than 7. To find the sum of these possible values, we can list them out:
a = 1, 2, 3, 4, 5, 6
Then, we add them up:
1 + 2 + 3 + 4 + 5 + 6 = 21
Hence, the sum of all possible values of a is 21.
To solve this problem, we need to find all the possible values of a which satisfy the given condition, and then find their sum.
The condition states that the sum of a and 5 should be less than 12. Mathematically, we can represent this as a + 5 < 12.
To isolate the variable a, we subtract 5 from both sides of the inequality: a < 12 - 5.
Simplifying the right side gives us: a < 7.
Now, we need to find all the positive integer values that are less than 7. These values are 1, 2, 3, 4, 5, and 6.
Finally, we find the sum of these values:
1 + 2 + 3 + 4 + 5 + 6 = 21.
So, the sum of all the possible values of a is 21.