in a family of 6 sister each born 3 years apart If the youngest sister is 10 years old how old is elder sister ?
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Answer:
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Answer ❤️
One thing we know for sure is that the product of the ages is 36 and also two of them have identical ages.
Without any other information its not possible to find out the exact 1 solution mathematically.
A good approach in solving will be prime factorization of 36.
Therefore, 36=2 x 2 x 3 x 3,
Now as 1 x any number= the same number,
We can write: 36= 2 x 2 x 3 x 3 x 1 x 1 = 2² x 3² x 1²
or as: 36 = 2 x 3 x 2 x 3 x 1 x 1 = 6 x 6 x 1² = 6² x 1²
Thus 36 is expressed as combination the products of squares of 4 different numbers.
So the age of the twins can be 1, 2, 3 and 6 (Since (2 x 3)² is also a factor)
Now let us see each case:
When twins are aged 1
1 x 1 x 36 = 36
When twins are aged 2
2 x 2 x 9 = 36
When twins are aged 3
3 x 3 x 4 = 36
When twins are aged 6
6 x 6 x 1 = 36
So these are the four solutions (1, 1, 36), (2, 2, 9), (3, 3, 4), (6, 6, 1).
However it must be kept in mind that these are the solutions if ages are considered to be whole numbers only. In case fractions are allowed there will be infinite number of solutions as something like (36, 36, 1/36) is also possible.