I need help with induction proof

Question

Prove by induction if Chicken McNuggets are sold in quantities of 6, 9, and 20, then the largest amount that cannot be purchased is 43.

Answer 1

Such problems are usually solved this way. Note that if you find ways to achieve every value from $44$ to $49$, the rest follow inductively by adding multiples of $6$. We take $$44=4\times 6+20,\,45=5\times 9,\,46=6+2\times 20,\\47=3\times 9+20,\,48=8\times 6,\,49=9+2\times 20.$$