Question

Ethan is 23 years older than Evan. If the

sum of Ethan and Evan's age is 43, how old
are Ethan and Evan?

Answer 1

Ethan is 33 and Evan is 10.

Explanation:

Givens

We are given that Ethan is 23 years older than Evan.

We are also given that the sum of their ages is 43.

We are told to find the ages of both Ethan and Evan.

Solve

First, create a system of equations.

`\texttt{Let} \ x \ \texttt{be Ethan's age and} \ y \ \texttt{be Evan's age:}\\\\\displaystyle \left \{ {{x+y=43} \atop {23+y=x}} \right.`

Then, substitute the value for x from the second equation into the first equation:

`x+y=43\\\\(23+y)+y=43\\\\23+2y=43\\\\23-23+2y=43-23\\\\2y=20\\\\\displaystyle (2y)/(2) = (20)/(2)\\\\y = 10`

Finally, substitute 10 as y into the second equation:

`23+y=x\\\\23+10=x\\\\33=x`

Final Answer

Therefore, Ethan is 33 and Evan is 10.