Question

The Johnson twins were born nine years after their older sister. This year, the product of the three siblings ages is exactly 1861 more than the sum of their ages. How old are the twins?

Answer 1

Answer: The age of the twins is 10 years.

Explanation:

Suppose the age of older sister be x

Let the age of twins sister be x-9, as they are born after 9 years.

Product of their ages be

`x(x-9)(x-9)\\\\=x(x^2-18x+81)\\\\=x^3-18x^2+81x`

Sum of their ages will be

`x+x-9+x-9\\\\=3x-18`

According to question,

`1861+3x-18=x^3-18x^2+81x\\\\x^3-18x^2+81x-3x+18-1861=0\\\\x^3-18x^2+78x-1843=0\\\\x=19`

So, Age of older sister will be 19 years.

Age of the twins will be

`19-9=10\ years`

Hence, the age of the twins is 10 years.