Ben is 202020 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 333 times as old as Daniel.

How old is Daniel now?

Daniel is 13 years old.

Step-by-step explanation:

Assign variables

let "x" be Ben's age now

let "d" be Daniel's age now

Create equations to represent the problem

x = d + 20 [1] Ben is 20 more than Daniel

x - 3 = 3 (d - 3) [2] Ben was 3d, 3 years ago.

Substitute the eq'n [1] into eq'n [2]

x - 3 = 3 (d - 3) Simplify first by distributing

x - 3 = 3d - 9 Substitute bolded 'x' with [1]

(d + 20) - 3 = 3d - 9 Isolate 'd' to solve problem

d + 20 = 3d - 6 Added 3 to both sides

20 = 2d - 6 Subtracted d from both sides

26 = 2d Added 6 to both sides

13 = d Divided both sides by 2, solved.

d = 13 Variable on left side for standard formatting

If you need to solve for Ben, use eq'n [1]

x = d + 20

x = 13 + 20 Substitute Daniel's age, d = 13

x = 33 Solved

Ben is 33.

Check the answer with this statement:

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

Three years ago, Ben was 30 and Daniel was 10.

30 is 3 times 10, or 30 = 3*10.

Therefore the answer is correct.