Lindsay is 5 years younger than Mark. Seven years ago, the sum of their ages was 31.

Let l be Lindsay's age and let m be Mark's age

The present age of Mark is 25 years.

And present age of Lindsay is 20 years.

Step-by-step explanation:

Let us assume:

The present age of Lindsay = l

The present age of Mark = m

⇒ Age of Lindsay seven years ago = (l - 7) years

and Age of Mark seven years ago = (m - 7) years

According to question:

Lindsay is 5 years younger than Mark ⇒ l = m - 5

Seven years ago, the sum of their ages was 31 ⇒ (l-7) + (m - 7) = 31

So, the given set of equation are:

l = m - 5 ... (1)

(l-7) + (m - 7) = 31

⇒ ((m - 5) - 7) + (m - 7) = 32 (from (1)

or, m - 12 + m - 7 = 31

or, 2m = 31 + 19 = 50

⇒ m = 50 / 2 = 25, or m = 25

Hence, the present age of Mark = 25 years

So, the present age of Lindsay = 25 - 5 = 20 years