Answer: 7 years old
Step-by-step explanation: The two quickest ways to solve these types of problems are by guess and check, and systems of equations. I will show you how to solve this problem with systems of equations since it is a systematic method.
We can replace the ages of Ethan and David with variables. Ethan's age is x and David's is y. Ethan is 3 years older than David and this can be represented by: y+3=x since 3 will have to be added to David's age, y to get Ethan's age, x. A second equation we can make is x+y=17 since the sum of their two ages is 17. Now we solve the system by first isolating a variable and then plugging that into the second equation.
y+3=x x is already isolated for us
x+y=17
(y+3)+y=17 We substitute x in the second equation for y+3
2y+3=17 Rearrange variables
2y=14
y=7 David's age, y, is 7.
Hope this helps!