Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 3 times as old as Daniel. How old is Daniel now?

Answer 1

First, establish variables at a point in time:

D = Daniel's age now [since we must solve for this]

B = Ben's age now

"Ben is 20 years older than Daniel" [now]

B = 20 + D [eq1]

"Ben and Daniel first met 2 years ago. [That's nice, but that information is not used.]

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

(B-3) = 3*(D-3) [eq2]

Solve for D: [this means to get rid of the B's in the equations]

((20+D) - 3) = 3(D-3) [putting eq1 into eq2]

20 + D - 3 = 3D - 9 [expand]

17 + D = 3D - 9 [collect terms[

-2D = -26 [subtract 17 from both sides]

D = 13 [divide both sides by -2]

Check:

B = 20 + 13 = 33

(B-3) = 3(13-3)

30 = 3(10)

30 = 30