Here's the question: "The sum of a number and it's double is 24.
Use the Guess and Check method to find the answer".

I don't know what her math book means by this. If they are being extreme about it they might want something like:

guess 10: double is 20, sum is 30, wrong.
guess 12: double is 24, sum is 36, wrong.
guess 3: double is 6, sum is 9, wrong.
guess 8...

A "numerical-computation" approach taking size into account would go more like:

guess 10: double is 20, sum is 30, too big.
guess 7: double is 14, sum is 21, too small.
guess 8...

There is a very old method they used to call "regula falsi" ("the wrong-answer rule") that would work for linear problems like this, never needing more than one wrong guess:

guess 10: double is 20, sum is 30; we wanted 24.

(24/30) x 10 is 8

Good hunting!
RD