The johnson twins were born eleven years after their older sister. this year, the product of the three siblings' ages is exactly 1181 more than the sum of their ages. how old are the twins?

So there are 3 siblings: the first twin, the second twin, and their older sister.

Since the sister is older by 11 years, you can represent their relationship with the following equation;
age of twin = age of older sister - 11
t = s - 11

Representing this next part may be a little hard to show, but i'll do my best :)

Adding the ages together can be represented like this;
total age = t + t + s
If the product of their ages ( t * t * s ) is 1181 more than the sum, you can show it like this:

Now you substitute in (s - 11) for t because s = t - 11.

Factor:
Since it's a third-degree equation, I just entered it into a polynomial solver in my calculator. There was only one factor listed, x = 19. Using (s - 19) = 0 as a factor, the equation becomes the following:

Using the quadratic formula, you get:


Since you have a square root of a negative number, the answer will be imaginary. You cannot have an age that is imaginary, so the age of the older sister (s) is 19 years.

Because t = s - 11, that means that t = (19) - 11 = 8.
t is the age of the twins, so the twins are 8 years old.