Question

trei elevi au impreuna 1500,dupa ce au cheltuit ,primul 75% din suma pe care o avea ,al doilea 80% din suma sa ,iar al treilea 2/3 din suma sa,le-au ramas sume egale.ce sumaa avut la inceput fiecare elev ?

Answer 1

[tex]\text{Notam cu x,y,z sumele celor trei elevi,iar t suma care le-a ramas.}\\ x+y+z=1500\\ [/tex]
[tex]\{x-\dfrac{75}{100}\cdot x=t ~~~~\{x-\dfrac{3}{4}\cdot x=t~~~~~\{\dfrac{x}{4}=t\\ \{y-\dfrac{80}{100}\cdot y=t \Leftrightarrow\{y-\dfrac{4}{5}\cdot y=t\Leftrightarrow\{ \dfrac{y}{5}=t \\ \{z-\dfrac{2}{3}\cdot z=t~~~~~~~~\{z-\dfrac{2}{3}\cdot z=t~~~~~\{\dfrac{z}{3}=t\\ \text{Obtinem deci ca:}\\ \dfrac{x}{4}=\dfrac{y}{5}=\dfrac{z}{3}=k\Rightarrow x=4k,y=5k,z=3k\\ 4k+5k+3k=1500\\ 12k=1500\Rightarrow k=125\\ x=4k\Rightarrow \boxed{x=500}\\ y=5k\Rightarrow \boxed{y=625}\\ z=3k\Rightarrow \boxed{z=375}[/tex]