Question

I can’t seem to understand this. I need 2 solutions and the work. If you could explain the work so I can do it in the future that would be great!!

Answer 1

Given:

Ethan is 23 years older than Evan

So, let Ethan is (x) years old

And Evan is (y) years old

So, the difference between them is 23 years old

so, x - y = 23

And the sum of Ethan and Evan's age is 43

so, x + y = 43

So, we have the following system of equations:

`\begin{gathered} x-y=23 \\ x+y=43 \end{gathered}`

add the equations to eliminate (y):

`\begin{gathered} (x-y)+(x+y)=23+43 \\ 2x=66 \\ x=(66)/(2)=33 \end{gathered}`

Now, substitute with (x) into the second equation to find (y):

`\begin{gathered} 33+y=43 \\ y=43-33=10 \end{gathered}`

So, the answer will be:

Ethan's age = x = 33

Evan's age = y = 10