SOLUTION: Ethan is 23 years older than Evan. If the sum of Ethan and Evan’s age is 43, how old are Ethan and Evan?

Click here to see ALL problems on Age Word Problems

Question 1176258: Ethan is 23 years older than Evan. If the sum of Ethan and Evan’s age is 43, how old are Ethan and Evan?
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
Ethan is 23 years older than.. Evan's "x" years
(x + 23) + x = 43
2x = 20
x = 10, Evan's age. Ethan is 33.
10 + 33 = 43 checks.
Wish You the Best in your Studies

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

First an informal solution using logical reasoning....

(1) Subtract 23 years from Ethan's age, making the two of them the same age; the sum of their ages is now 43-23 = 20.
(2)That means the age of each of them is 20/2 = 10 years.
(3) Now add those 23 years back on to Ethan's age, making his age 10+23 = 33.
ANSWERS: Ethan is 33; Evan is 10.

With formal algebra....

let x be Evan's age
then x+23 is Ethan's age

The sum of their ages is 43:

ANSWERS:
Evan's age: x = 10
Ethan's age: x+23 = 33

Observe that the formal algebra does EXACTLY the same calculations as the solution using logical reasoning....