David went to the market yesterday, he bought some stuff by $107$ shikels, when he opend his wallet to pay for the stuff, he saw different types of money, $1$ shikel, $10$ shikel, and $50$ shikel. How many ways can he pay the $107$ shikels? Assuming that there are enough amount of all types of money.
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The problem "how many ways to make change for a dollar" is well known, and you can easily find discussions online (here for instance). The same techniques will apply here. – lulu Oct 26 '17 at 11:55
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have you heard about generating functions? – Vinyl_cape_jawa Oct 26 '17 at 12:04
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$$1\cdot x+10\cdot y+50\cdot z=107$$ $$x+10y+50z=107$$ where $x,y,z\ge0, x,y,z \in \mathbb Z$
$z\le 2$
1) Let $z=2$, then $$x+10y=7$$ Then $x=7, y=0$
$$(x=1, y=0, z=2)$$
2) Let $z=1$
3) Let $z=0$
Can you finish?
Roman83
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