Question 1176258
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First an informal solution using logical reasoning....<br>
(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.<br>
With formal algebra....<br>
let x be Evan's age
then x+23 is Ethan's age<br>
The sum of their ages is 43:<br>
{{{(x)+(x+23) = 43}}}
{{{2x+23 = 43}}}
{{{2x = 20}}}
{{{x = 10}}}<br>
ANSWERS:
Evan's age: x = 10
Ethan's age: x+23 = 33<br>
Observe that the formal algebra does EXACTLY the same calculations as the solution using logical reasoning....<br>