Lucas' mom is eight years older than twice his age. The sum of their ages is 77. How old are Lucas and his mom?

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