Find all sets of four consecutive even whole numbers whose sum is less than 35
Find ALL? I can probably think of one or two....
2, 4, 6, 8, 10, 12, 14, 16, 18
What do you think?
To find all sets of four consecutive even whole numbers whose sum is less than 35, we can follow these steps:
1. Let's assume the first number in the set is x. Since we need four consecutive even numbers, we know that the next three even numbers will be x + 2, x + 4, and x + 6.
2. Now, we need to find the sum of these four numbers and ensure that it is less than 35:
x + (x + 2) + (x + 4) + (x + 6) < 35
3. Simplify the equation:
4x + 12 < 35
4. Subtract 12 from both sides:
4x < 23
5. Divide both sides of the inequality by 4:
x < 23/4
6. Since we are dealing with whole numbers, the first number (x) must be less than 23/4 and a whole number. This means that x can be either 0, 1, 2, or 3.
7. Plug these values into the equation x + (x + 2) + (x + 4) + (x + 6), and check if the sum is less than 35:
- For x = 0: 0 + 2 + 4 + 6 = 12 (less than 35)
- For x = 1: 1 + 3 + 5 + 7 = 16 (less than 35)
- For x = 2: 2 + 4 + 6 + 8 = 20 (less than 35)
- For x = 3: 3 + 5 + 7 + 9 = 24 (greater than 35)
8. So, there are three sets of four consecutive even whole numbers whose sum is less than 35: {0, 2, 4, 6}, {1, 3, 5, 7}, and {2, 4, 6, 8}.