Question 353960
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 {{{x+y=10}}}



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 {{{y=2(x+2)}}}



{{{x+y=10}}} Start with the first equation.



{{{x+2(x+2)=10}}} Plug in {{{y=2(x+2)}}}



{{{x+2x+4=10}}} Distribute.



{{{3x+4=10}}} Combine like terms on the left side.



{{{3x=10-4}}} Subtract {{{4}}} from both sides.



{{{3x=6}}} Combine like terms on the right side.



{{{x=(6)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=2}}} 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).



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Because {{{y=2(x+2)}}} and {{{x=2}}}, we can use this to find the first number of the second list.



So {{{y=2(2+2)=2(4)=8}}} 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



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Jim