Renee Tysinger, 7/17/16, Weekly Problem #4

What three consecutive even integers have a sum of 150? Can you find three consecutive odd integers that add up to 150?

Strategy #1

1st integer: x --------------------------- 48

2nd integer: x + 2 --------------------- 50

3rd integer: x + 4 ---------------------- 52

x +  (x + 2) +  (x + 4) = 150

3x + 6 = 150

      - 6      -6

----------------

3x = 144

---     ----

3         3

x = 48

Strategy #2

150/3 = 50 ----- middle number

3 integers --> 48, 50, 52

The first strategy that I implemented to find the three consecutive even integers involved an algebraic equation. I used an expression to represent each unknown even integer. I let x represent the first unknown integer. Since the second integer must be both even and consecutive, I let x + 2 represent it. the reason that I added 2 is because all even integers are 2 values apart. For example, 2 and 4 are even consecutive integers. For the third integer I used x + 4. This is because the third integer must also be even and consecutive in relation to the first 2 values. For instance, take the consecutive even integers 2, 4, 6. 4 is 2 away from the starting value and 6 is 4 away from the starting value. Next I added the three expressions together and set them equal to 150. After combining like terms and using inverse operations to isolate the variable, I discovered that the first integer would be 48. This means that the other 2 consecutive integers would be 50 and 52.

For the second strategy I used simple division to find the average, or the middle, of the three values. I divided 150 by 3 since we must divide the sum of the values by the number of values in order to determine the average. This resulted in an average of 50 for the middle value. The other two consecutive integers thus consists of the consecutive even integers to the left and right of 50. This strategy leads us to the same 3 numbers as the first strategy, 48, 50, and 52.

I was unable to find 3 consecutive odd integers with a sum of 150. The sum of 3 odd integers will be odd and 150 is an even number. To test this I chose 2 sets of 3 consecutive odd integers near the 3 consecutive even integers listed above. The first set is too small and the second set is too large.

47 + 49 + 51 = 147                           49 + 51 + 53 = 153