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.

Answer 1

Answer:

Ben is 33 years old

Step-by-step 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

Step-by-step 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