Let's let x represent Justin's age and y represent Julia's age. Since we know that Justin is 2/5 of Julia's age, we can write:
x = 2/5 y
Also, since we know that Julia is 27 years older than Justin, we can write:
y = x + 27
We an now solve these 2 equations with 2 unknowns using substitution. Substitute x in the second equation with 2/5 y from the first equation:
y = 2/5 y + 27
Now we can solve for y (or Julia's age) using inverse operations:
Subtract 2/5y from both sides of the equation:
y-2/5 y = 2/5 y + 27 - 2/5 y
Combine like terms:
3/5 y = 27
Multiply both sides of the equation by the reciprocal of 3/5 (or 5/3):
5/3 * 3/5 y = 27 * 5/3
Since 27 * 5/3 is equivalent to 45:
y = 45 years old
So Julia is 45 years old. Justin will be 27 years younger or 18 years old.
