Answer:
Age of Lucas = 23 years
Age of Lucas Mom = 54 Years
Step-by-step explanation:
In this question we have to find the age of Lucas and his Mom
Let the age of Lucas be x
According to given condition
Twice of his age 2 * x =2x
Eight years older means age + 8x
So
Age of his mom = Twice of his age + 8
= 2x + 8 .................(ii)
now according to second condition
Age of Lucas + Age of his mom = 77
Put the values in the condition above
x + (2x + 8) = 77
x + 2x + 8 =77
3x + 8 = 77
subtracting 8 from both sides
3x + 8 - 8 = 77 -8
3x = 69
Dividing both sides by 3
x = 69 / 3
x = 23 years
Age of Lucas = 23 years
Now from equation (i)
Age of Lucas Mom = 2(x) + 8
putting in the value we get
Age of Lucas Mom = 2 ( 23) + 8
=46 + 8
=54 Years
Age of Lucas Mom = 54 Years
and 
