Question Number 212209 by efronzo1 last updated on 06/Oct/24
$$\:\:\:\cancel{\underbrace{\gtrdot}}\: \\ $$
Answered by som(math1967) last updated on 06/Oct/24
$$\:{let}\:{no}\:{of}\:{solders}\:{in}\:{A},{B},{C}\:{are} \\ $$$${x},{y},{z} \\ $$$$\therefore\mathrm{37}{x}+\mathrm{23}{y}=\mathrm{29}{x}+\mathrm{29}{y} \\ $$$$\Rightarrow\:\mathrm{8}{x}=\mathrm{6}{y}\Rightarrow\:{x}:{y}=\mathrm{3}:\mathrm{4} \\ $$$$\:\mathrm{23}{y}+\mathrm{41}{z}=\mathrm{33}{y}+\mathrm{33}{z} \\ $$$$\Rightarrow\mathrm{10}{y}=\mathrm{8}{z}\Rightarrow{y}:{z}=\mathrm{4}:\mathrm{5} \\ $$$$\therefore{x}:{y}:{z}=\mathrm{3}:\mathrm{4}:\mathrm{5} \\ $$$$\:{say}\:{x}=\mathrm{3}{k},{y}=\mathrm{4}{k},{z}=\mathrm{5}{k} \\ $$$$\:{average}\:{all}\:{solders} \\ $$$$=\frac{\mathrm{37}×\mathrm{3}{k}+\mathrm{23}×\mathrm{4}{k}+\mathrm{41}×\mathrm{5}{k}}{\mathrm{3}{k}+\mathrm{4}{k}+\mathrm{5}{k}} \\ $$$$=\frac{\mathrm{111}{k}+\mathrm{92}{k}+\mathrm{205}{k}}{\mathrm{12}{k}} \\ $$$$=\mathrm{34} \\ $$