Question

ellen is x years old her mother age is square of her age. if ellen's father is 2 years older than her mother and the sum of all three ages is 80 years old , how old is ellen

Answer 1

Ellen must be 6 years old. We determined this by setting up an equation to represent the given relationship between her age, her mother's age as the square of her own, and her father being two years older than her mother, with the total sum being 80 years.

Step-by-step explanation:

The question asks us to find the age of Ellen when given the relationship between her age, her mother's age, and her father's age. Let Ellen's age be represented by x, then her mother's age is x^2 (the square of Ellen's age), and her father's age is x^2 + 2 years. The sum of their ages is given as 80 years. To find Ellen's age, we can set up the following equation:

x + x^2 + (x^2 + 2) = 80

This simplifies to:

2x^2 + x + 2 = 80

Subtracting 80 from both sides of the equation gives us:

2x^2 + x - 78 = 0

Now we have a quadratic equation that we can solve by factoring, using the quadratic formula, or through graphing. The factors of -78 that add up to 1 are 12 and -6.5. Therefore, we can express the equation as:

(2x - 12)(x + 6.5) = 0

This gives us two potential solutions for x:

x = 6 or x = -6.5

Since age cannot be negative, Ellen must be 6 years old.