SOLUTION: I am checking my sons math. Find four consecutive even integers such that 6 time the sum of the first and second is 8 more than 10 times the fourth. Rob Dewey...Mitchell's Da

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Question 252619: I am checking my sons math.
Find four consecutive even integers such that 6 time the sum of the first and second is 8 more than 10 times the fourth.
Rob Dewey...Mitchell's Dad.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive even integers follow the form: x, x+2, x+4, x+6, etc...

So because "6 time the sum of the first and second is 8 more than 10 times the fourth", this translates to 6%28x%2Bx%2B2%29=10%28x%2B6%29%2B8


6%28x%2Bx%2B2%29=10%28x%2B6%29%2B8 Start with the given equation.


6x%2B6x%2B12=10x%2B60%2B8 Distribute.


12x%2B12=10x%2B60%2B8 Combine like terms on the left side.


12x%2B12=10x%2B68 Combine like terms on the right side.


12x=10x%2B68-12 Subtract 12 from both sides.


12x-10x=68-12 Subtract 10x from both sides.


2x=68-12 Combine like terms on the left side.


2x=56 Combine like terms on the right side.


x=%2856%29%2F%282%29 Divide both sides by 2 to isolate x.


x=28 Reduce.


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Answer:

So the solution is x=28 which means that the four consecutive even integers are

x = 28
x+2 = 30
x+4 = 32
x+6 = 34