I need step by step instructions to help explain solving the below problem to my sixth grader

Question

You and your friend play a trivia game. You answer 55% of the questions correctly and your friend answers 60% of the questions correctly. What is the minimum number of questions in the game?

Answer 1

I can think of a trial and error way of solving this. You know the total number of questions must be an integer. You also know that 55% and 60% of that total must also be integers. Suppose the total number of questions is n.

55% of n is 0.55n

60% of n is 0.60n

The problem becomes finding the smallest integer n such that 0.55n and 0.60n are also integers. By trial and error,

0.55 x 1 = 0.55

0.55 x 2 = 1.1

...

0.55 x 19 = 10.45

0.55 x 20 = 11

I found that n must be at least 20 to make 0.55n an integer. Now test this value of n with 0.60.

0.60(20) = 12

It looks like 20 is the answer. There may be another way of solving this without trial and error, but it does not occur to me at this time.