Question

Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 33 times as old as Daniel.

how old is Ben now?

Answer 1

Ben is 33 years old

Explanation:

Let Ben’s age = B

Let Daniel’s age = x

B = x + 20 (20 years older than Daniel)

Their ages 3 years ago:

B = 3x (also given in problem)

B = x + 20 (given in problem)

x + 20 = 3x (Since both equations are equal to B, set them equal to each other)

20 = 2x (simplify)

x = 10

B = 10 + 20 = 30

Their ages now:

Add 3 to their "ages three years ago"

New x = Daniel’s age = old age + 3 = 10 + 3 = 13 years old

B = Ben’s age = old age + 3 = 30 + 3 = 33 years old

Answer 2

Answer: 33

Explanation:

Today 3 years ago

Ben: x + 20 (x + 20) - 3

Dan: x x - 3

3 years ago, Ben was 3 times as old as Daniel

⇒ (x + 20) - 3 = 3(x - 3)

x + 17 = 3x - 9

17 = 2x - 9

26 = 2x

13 = x

Today, Ben = x + 20

= 13 + 20

= 33