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# Set up the equation?

John has two lists of consecutive numbers. The first two numbers of each list equal ten. If the third number in the second list times 2 plus 8 = the sum of the first list, what are the numbers in the two lists? The answer is 6--8-10 and 4-6-8. Need help understanding how to set up the equation.

Judy, according to the answer you gave us, you missed very important word: "John has two lists of consecutive even numbers."

The first list of even number is 2n , 2n + 2 , (2n + 2) + 2
The second list is (10 - 2n) , (10 - 2n) + 2 , ((10 - 2n) + 2) + 2
↑                                               ↑
because "the sum of first two numbers of each list equal ten"    ↑
↑
the third number in the second list
2{((10 - 2n) + 2) + 2} + 8 = 2n + (2n + 2) + ((2n + 2) +2)
2 (10 - 2n + 4) + 8 = 6n + 6
20 - 4n + 8 + 8 = 6n + 6
36 - 4n = 6n + 6
-4n - 6n = -36 + 6
-10n = -30 ----> n = 3
First list: 2 × 3 = 6
8
10
Second list: 10 - 6 = 4
6
8

Judy, this is a trick question. No two consecutive numbers equal 10 when added, subtracted, multiplied or divided together. This is most likely the best reason there is no equation to formulate. Good luck.