Question Number 116700 by bemath last updated on 06/Oct/20
$$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integral}\: \\ $$$$\mathrm{solutions}\:\mathrm{does}\:\mathrm{3x}+\mathrm{5y}=\mathrm{300}\:\mathrm{have}? \\ $$
Answered by mr W last updated on 06/Oct/20
$${x}=\mathrm{5}{p} \\ $$$${y}=\mathrm{3}{q} \\ $$$${p}+{q}=\mathrm{20} \\ $$$${p}=\mathrm{1},\mathrm{2},...,\mathrm{19}\:\Rightarrow\mathrm{19}\:{solutions}! \\ $$
Commented by bemath last updated on 06/Oct/20
$$\mathrm{yes}...\mathrm{gave}\:\mathrm{kudos} \\ $$