SOLUTION: Find four consecutive integers so that if the first is increased by 2, the second decreased by 2, the third multiplied by 2 and the fourth divided by 2, then the sum of the four re

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Question 357188: Find four consecutive integers so that if the first is increased by 2, the second decreased by 2, the third multiplied by 2 and the fourth divided by 2, then the sum of the four resulting numbers is 200.
Found 2 solutions by stanbon, neatmath:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find four consecutive integers so that if the first is increased by 2, the second decreased by 2, the third multiplied by 2 and the fourth divided by 2, then the sum of the four resulting numbers is 200.
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1st: x-1
2nd: x
3rd: x+1
4th: x+2
-------------------------
Equation:
x-1+2 + x-2 + 2(x+1) +(x+2)/2 = 200
----
x +1 + x - 2 + 2x+2 + (x+2)/2 = 200
4x +1 + (x+2)/2 = 200
8x+2 + x+2 = 400
9x + 4 = 400
9x = 396
x = 44
----
1st: 39
2nd: 40
3rd: 41
4th: 42
===============
Cheers,
Stan H.

Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

We know that four unknown consecutive integers would be in the form:

x x%2B1 x%2B2 x%2B3

So, we then use this format to solve the problem, given:

%28x%2B2%29%2B%28x%2B1-2%29%2B2%2A%28x%2B2%29%2B%28x%2B3%29%2F2=200

2x%2B1%2B2%2A%28x%2B2%29%2B%28x%2B3%29%2F2=200

2x%2B1%2B2x%2B4%2B%28x%2B3%29%2F2=200

4x%2B5%2B%28x%2B3%29%2F2=200

8x%2B10%2B%28x%2B3%29=400

9x%2B13=400

9x=387

x=43

Thus, the four consecutive integers we are looking for are:

43, 44, 45, and 46

I hope this helps!