Question

we make 1 square with 4 matches, 2 squares with 7 matches and 3 squares with 10 matches.How many squares canwe make with 100 matches ?

Answer 1

You start with 4 matches, then you add only three more to get another (attached to the fist one) square. Then each time to get one more square you add 3 more matches.

Now, let x be a number of squares you can make from a given number of matches. Then
4+3*(x-1)=100. I used (x-1) because 4 represents first square, so we need exactly total number of squares possible minus one.

You can check that it works by trying other numbers:

4+3*(x-1)=4 - 1square from 4 matches
4+3x-3=4
1+3x=4
3x=3
x=1 (square) exactly what you had.

4+3*(x-1)=7
4+3x-3=7
1+3x=7
3x=6
x=2 (squares)

You can check other numbers yourself.