Question

qual a fração aquivalente a 3/5 , cuja soma dos termos e 40?

Answer 1

$\left \{ {{x+y=40} \atop {\frac{x}{y}=\frac{3}{5}}} \right. \left \{ {{y=40-x} \atop {5x=3y}} \right. \left \{ {{y=40-x} \atop {5x=3(40-x)}} \right. \Rightarrow \left \{ {{y=40-x} \atop {5x=120-3x}} \right. \Rightarrow \left \{ {{y=40-x} \atop {5x+3x=120}} \right. \Rightarrow \left \{ {{y=40-x} \atop {8x=120}} \right. \left \{ {{y=40-x} \atop {x=\frac{120}{8}}} \right. \left \{ {{y=40-x} \atop {x=15}} \right. \left \{ {{y=40-15} \atop {x=15}} \right. \Rightarrow \left \{ {{y=25} \atop {x=15}} \right.$