# 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 =...

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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.

Approved by eNotes Editorial Team

The woman is x years old. As her brother is 4 years older than her, his age is x + 4.

The product of their ages is 1020.

So we have x*(x + 4) = 1020

x^2 + 4x = 1020

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

=> x^2 + 34x - 30x - 1020 = 0

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

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

x = -34 and x = 30

We can eliminate the negative root.

This gives the age of the woman as 30 years.

Approved by eNotes Editorial Team