SOLUTION: I always have problems with these word problems: Find three consecutive even numbers so that the sum of the first and third numbers is 22 less than three times the second number. T

Question 525: I always have problems with these word problems: Find three consecutive even numbers so that the sum of the first and third numbers is 22 less than three times the second number. This one is hard, I would love it if you helped me out on this please and thank you!
Kelsie
Found 2 solutions by arden42, jseal2001:
Answer by arden42(16) (Show Source): You can put this solution on YOUR website!
Well, first we need to assign letters to each of the numbers. x, y and z will do.
Now, if they are consecutive even numbers, then we know that x is 2 less than y, and y is 2 less than z:

We'll rearrange the second one to be consistent:

Now for the rest of the question. The first number plus the third number is 22 less than the second number multiplied by 3:

To work out the numbers, we will need to substitute the first 2 equations into the third, like this:

Expanding the brackets gives:

Adding 22 to both sides, and taking away 2y from both sides:

So the middle number is 22. Since the other numbers are the even numbers either side of it, the final answer is:
The 3 numbers are 20, 22 and 24.
Answer by jseal2001(1) (Show Source): You can put this solution on YOUR website!
important to note 3 consecutive even numbers
1st number =x example 1st number =2, next number x+2 =4, next number x+4=6
2nd number =x +2
3rd number =x +4
sum of 1st and 3rd = 3 times of 2nd number - 22
so x + x+4 = 3(x+2) - 22
2x + 4 = 3x +6 - 22
2x -3x = 6 - 22 -4
-x = -20
answer x =20
so 1st number = 20
2nd number = 22
3rd number = 26
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