How to answer this questions in two different ways: using a table and guess and check method.

Question

How to answer this questions in two different ways: using a table and guess and check method.

Points are scored for each medal won in a competition. 

The Rockets won a total of 16 medals and scored 36 points. 6 of their medals were Silver. 

How many Gold medals did the Rockets win? 

Medal	Points per medal
gold	3
silver	2
Bronze	1

The correct answer is 8 gold medal

6x2=24 points

36-12=24 points

3/24=8 gold medals

but how can I solve this by table and by guess and check

Answer 1

g + s + b = 16, g + 6 + b = 16, g + b = 10, b = 10 - g

3g + 2(6) + 1b = 36

3g + b = 24

b = 24 - 3g

24 - 3g = 10 - g

-2g = -14

g = 7

b = 3

I did not get g = 8, which you say is the correct answer, yet, I can't find a flaw in my approach.

7 + 6 + 3 = 16 Check!

7(3) + 6(2) + 1(3) = 36

21 + 12 + 3 = 36 Check!

My answer is correct.