Hi,

1900 in Montgomery County, City of Kendall, Alabama

Cook, Edmond Head born Apr 1870 age 30 Married 6 years AL AL AL
Cook, Caroline Wife born June 1876 age 23 Married 6/3 children born 3 living AL AL AL
Cook, Joseph Son born Feb 1894 age 6 AL AL AL
Cook, Edmond Son born Aug 1896 age 3 AL AL AL
Cook, Richard Son born Dec 1899 age 6 months AL AL AL

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1910 in Lowndes County Alabama

Cook, Edmond Head age 40 Married 16 years AL/Unknown/AL
Cook, Caroline WIfe age 36 Married 16 years 3 children born 3 living
Cook, Joseph Son age 15 AL AL AL
Cook, Edmond JR. Son age 13 AL AL AL
Cook, James Son age 11 AL AL AL

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1920 in Lowndes County of Pintlala, Alabama

Cook, Edd Head age 50 Al/Ga/AL
Cook, Caroline age 45 AL/Al/AL
Cook, James age 19

Next door is>

Cook, Edmon Head age 24
Cook, Elvira Wife age 20
Cook, Alice May dau age 11 months

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1930 in Lowndes County, Pintlala, Ala

Cooks, Edd Head 59 /age at first marriage is 22/ Al Al AL
Cooks, Caroline Wife age 50 age at first marriage 18/ Al Al Al
Cooks, Alice Granddau age 13 Al AL AL
Cooks, Caroline Granddau age 5 Al AL AL
Cooks, L? Granddau age 4 AL AL AL

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Note that I did not find a Eugene or a Eli as a child of Edmond and Caroline. Each census stated that she only had three children and they were listed as Joseph, Edmond Jr, and Richard/James.

Also, I could not find Edmond Jr in 1930 but one of his children (Alice) was living with his father, Edmond Sr.

I hope this helps

Tony