Find 4 consecutive integers whose sum is 17798.
Solution
The four numbers will each be about 1/4 of 17798, which is 4449.5. Take two numbers on each side of 4449.5 and you'll have 4448, 4449, 4450, and 4451.
Or, Algebraically, let the numbers be x, x + 1, x + 2, and x + 3. Then we can write the equation x + (x + 1) + (x + 2) + (x + 3) = 4x + 6 = 17798, and go from there.
This is one of those problems where Algebra students might balk at making an equation if they can find the numbers without it. I think it best to honor this balking but also to say "here's what you can do if you're stuck." And then show them the equation.