Family planning
Algebra
Level
3
My mother dreamed of having nineteen children however her dream didn't come true. But I have three times as many sisters as first cousins, and I have half as many brothers as sisters. How many children did my mother have?
This is just a fictitious story.
The answer is 10.
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1 solution
Number of sisters is a multiple of three over first cousins, and a multiple of two over brothers.
So, I have 6, 12, 18, 24, . . . sisters, and 9, 18, 27, .. . siblings altogether. Add one for myself to get the total number of children: 10, 19, 28, . . .
If my mother's dream of 19 children not coming true means that she has LESS than 19 then we are left with an answer of 10 children.