A woman is x years old. Her brother is four years older than her. The product of their ages is 1020. What is her age?

Given that the woman's age is
x.

Let us assume that the brother's age is
y.

Given that the brothers age is 4 years older than
her.

Then we will rewrite:

y=
x+ 4 ................(1)

Also given that the product of
their ages is 1020.

Then we will
write:

x*y = 1020
............(2)

Now we will use the substitution method to
solve for x and y.

==> x*(x+4) =
1020

==> x^2 + 4x =
1020

==> x^2 + 4x - 1020 =
0

Now we will
factor:

==> (x - 30 ) (x+34) =
0

==> x1= 30 ==> y1= 30+4 =
34

==> X2= -34 ( NOT
VALID)

Then the woman's age is 30 years
old.