Answer:
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.
