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!

First off, if:
$$S=40a+50b$$
then:
$$S+10=40(a-1)+50(b+1)$$
but only if $a\ge1$. If $a=0$ and $b\ge 3$, then:
$$S+10=40\cdot4+50(b-3)$$
So, if $S\ge150$, we can form $S+10$ if we can form $S$. Now, something similair can be done for $S+5$. After you've got that figured out, use induction to prove you can reach all multiples of $5$ greater than a certain number (what number?) and prove that you can only reach multiples of $5$ (why?)
Then you're left with the small cases, which you'll need to check by hand
