Question 1199605: The sun of Anna's age and Ben's age is 40.Two years ago, Anna was thrice as Ben. Find the Anna's age Found 3 solutions by math_tutor2020, josgarithmetic, greenestamps:Answer by math_tutor2020(3817) (Show Source):
The sum of these current ages is 40.
A+B = 40
Pick A or B to isolate. I'll solve for B.
B = 40-A
A-2 = Anna's age two years ago
B-2 = Ben's age two years ago
Two years ago, Anna was thrice as Ben.
A-2 = 3(B-2)
Apply substitution and solve for "A".
A-2 = 3(B-2)
A-2 = 3(40-A-2) ...... replace B with 40-A
A-2 = 3(38-A)
A-2 = 114-3A
A+3A = 114+2
4A = 116
A = 116/4
A = 29
Anna is currently 29 years old.
B = 40-A
B = 40-29
B = 11
Ben is currently 11 years old.
Rewind the clock 2 years.
Anna was 29-2 = 27 years old.
Ben was 11-2 = 9 years old.
We see that Anna's past age is exactly triple that of Ben's past age (3*9 = 27).
The answer is confirmed.
You have received two responses, both showing a typical solution using two variables, and setting up the problem using the information exactly as given.
Both solution methods are fine; however, the amount of work required to reach the final answer can be a lot less if you take the time to analyze the given information and set up the problem for solving using a single variable.
Here is how I would set up and solve the problem.
let x = Ben's age 2 years ago
then 3x = Anna's age 2 years ago
(