There's a WWI Draft Registration card on Ancestry.com for Leo Ellsworth Cook
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World War I Draft Registration Cards, 1917-1918 about Leo Ellsworth Cook
Name: Leo Ellsworth Cook
County: Warren
State: Pennsylvania
Birth Date: 12 May 1900
Race: White
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There's a ton of census records for Leo Cook or Leo E Cook - using the birth date from the WWI draft record, the census results suggest his mother's name was probably Mary, not Amanda.
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1920 United States Federal Census about Leo E Cook
Name: Leo E Cook
Home in 1920: Kellettville, Forest, Pennsylvania
Age: 20
Estimated Birth Year: abt 1900
Birthplace: Pennsylvania
Relation to Head of House: Son
Father's Name: Daniel M Cook
Father's Birth Place: Pennsylvania
Mother's Name: Mary M Cook
Mother's Birth Place: Pennsylvania
Marital Status: Single
Race: White
Sex: Male
Able to read: Yes
Able to Write: Yes
Household Members:
Name Age
Daniel M Cook 59
Mary M Cook 55
Lester E Cook 27
Maccie A Cook 23
James M Cook 21
Leo E Cook 20
Martha Cook 16
Carl E Cook 13
Cleveland Reed 27
Robert J Cook 36
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Quote:
1900 United States Federal Census about Leo E Cook
Name: Leo E Cook
Home in 1900: Barnett, Jefferson, Pennsylvania
[Heath, Jefferson, Pennsylvania]
Age: 1
Birth Date: May 1899
Birthplace: Pennsylvania
Race: White
Gender: Male
Relationship to head-of-house: Son
Father's Name: Daniel Cook
Father's Birthplace: Pennsylvania
Mother's Name: Mary A Cook
Mother's Birthplace: Pennsylvania
Marital Status: Single
Household Members:
Name Age
Daniel Cook 30
Mary A Cook 30
Edward L Cook 8
Bertha E Cook 5
Mackey A Cook 5
James M Cook 3
Leo E Cook 1
William P Hannold 14
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From those, we know Daniel was born around 1870 in PA - searching for him brings up a result on a public tree which suggests the mother was Mary Amanda Rossey, b. 1868 in PA. No parents for Daniel but Mary's parents were Peter Rossey b. 1836 in PA and Lucinda Showers b. 1840 in PA. Granted, public trees are not necessarily accurate but they serve as a good starting point or clue in your research.
There are 1870 and 1880 censuses for a Daniel M Cook born about 1867 but he is listed as Black on both of them whereas he's listed as white on the above records so I doubt it's the same man unless he was a "mulatto" who could pass for white (or unless the transcriptions are wrong or something).
Also try searching:
https://familysearch.org/ - it's the biggest free records database on the net.