How old is anna and how old is laura

Question

anna is 3 years older than laura. the product of their ages is double the sum of their ages. 

Answer 1

Let A = Anna's age (yr)

     L = Laura's age (yr)

 

Need 2 independent equations to solve for the 2 unknowns, A and L

 

1)    A = L + 3

 

2)    A*L = 2*(L + A) 

 

Substitute equation 1) into equation 2) and solve for L:

 

(L + 3)*L = 2*L + 2*(L + 3)

 

L² + 3*L = 2*L + 2*L + 6

 

L² - L - 6  = 0      (factor quadratic equation)

 

(L - 3)(L + 2) = 0

 

L = 3 yrs   (Laura's age )         (she cannot be negative age, L = -2, which is other root)

 

A = L + 3 = 3 + 3  = 6 yrs    (Anna's age)