SOLUTION: Jane has two lists of three consecutive even numbers. the sum of the first number on each list is 10. If twice the second number on the first list has the same value as the first

Question 353960: Jane has two lists of three consecutive even numbers. the sum of the first number on each list is 10. If twice the second number on the first list has the same value as the first number on the second list, what are the two sets of consecutive even numbers?
I need help setting up the problem. The second sentence is confusing because I'm not sure if they mean the sum of both 1st numbers on both lists or the digits themselves totalling 10 (like 28, which could be 2+8 = 10). Please help.
Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let

x = first number on first list

and

y = first number on second list

So this means that the first list is: x, x+2, x+4

and the second list is: y, y+2, y+4

We're given that "the sum of the first number on each list is 10", which simply means that

We're also told that "twice the second number on the first list has the same value as the first number on the second list" which means that

Start with the first equation.

Plug in

Distribute.

Combine like terms on the left side.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the first number of the first list is 2. So the first list is 2, 4, 6 (add 2 to each successive number).

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

Because and , we can use this to find the first number of the second list.

So which means that the first number on the second list is 8. Also, notice how the first number of the first list (2) and the first number of the second list (8) add to 10 (2+8=10)

So the second list is 8, 10, 12

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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