$$x,y,z \in \{0,1,2,3,4,\ldots\}, 50x+25y+10z=2000$$ I have no clue to this form of equation . But I can solve by two variable . This is multiple choice question $$703\\716\\820\\861$$ Can anyone help me?
2026-04-25 07:36:55.1777102615
How many solution are possible for $x,y,z \in \{0,1,2,3,4,...\} , 50x+25y+10z=2000$?
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$$\quad{50x+25y+10z=2000\div5\\10x+5y+2z=400\\\implies y=2y'\\z=5z' }$$now $$\quad{x,y',z' \in \{0,1,2,3,4,5...\}\\10x+5(2y')+2(5z')=400\\x+y'+z'=40\\\begin{pmatrix} 40+3-1 \\ 3-1 \end{pmatrix} =\frac{42\times 41}{2}=861}$$