Strong Induction to find all possible combinations of two numbers Full disclosure, this is a homework question, so I'm only looking for hints not full solutions please. 
There is a store which offers two denominations of gift certificates, \$25 and \$40. Determine the possible total amounts that can be formed using the certificates, using strong induction to prove your answer.  
My first approach was to write out something like this, let $S$ be a possible amount where $S = 25a + 40b$ and $a, b \in \mathbb{Z}^+$ ($0$ being included in the positive integers). The problem is that I'm not sure how to use this as a propositional statement for strong induction.  
Second, I tried to make a table to find a pattern, like this:
$$
\begin{array}{c|ccccc}
0 & 0 & 1 & 2 & 3 & 4 \\
\hline
0 & 0 & 25 & 50 & 75 & 100 \\
1 & 40 & 65 & 90 & 115 & 140 \\
2 & 80 & 105 & 130 & 155 & 180 \\
3 & 120 & 145 & 170 & 195 & 220 \\
4 & 160 & 185 & 210 & 235 & 260 \\
\end{array}
$$
The issue with this approach was that, once again, I could see no particular path towards using strong induction (or any discernible pattern).  
I'm not sure how best to move forward, and I haven't been able to find many helpful resources. I'd be very grateful for some help, thanks!

Since you are only looking for a hint:
HINT Expand your table by just two more columns, and then look at your table and start writing the possible total amounts in order. So you get 25, 40, 50, 65,  75, 80, .... After a while you will see a pattern ... Use this to form your hypothesis and prove by strong induction.
