Anna is 3 years older than Laura. The product of thier ages is double the sum of thier ages. How old are they?
Anna Age-6
Laura Age-3
Product= 6*3=18
Sum=6+3=9
189
To find the ages of Anna and Laura, we can use algebraic equations. Let's represent Laura's age as "x".
According to the information provided, Anna is 3 years older than Laura. Therefore, Anna's age can be represented as "x + 3".
The problem states that the product of their ages is double the sum of their ages. So, we can set up the following equation:
(x)(x + 3) = 2(x + (x + 3))
Let's solve the equation to find the ages.
Expanding the equation:
x^2 + 3x = 2(2x + 3)
Simplifying further:
x^2 + 3x = 4x + 6
Rearranging the terms:
x^2 - x - 6 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula.
Factoring the equation:
(x - 3)(x + 2) = 0
Setting each factor equal to zero:
x - 3 = 0 or x + 2 = 0
Solving for x:
x = 3 or x = -2
Since age cannot be negative, we discard the x = -2 solution.
Therefore, Laura's age is x = 3.
Since Anna is 3 years older than Laura, Anna's age is 3 + 3 = 6.
Therefore, Laura is 3 years old and Anna is 6 years old.