Răspuns:
[tex]\color{orangered}\Large\boxed{\bf 125~lei~ prima~ persoana}[/tex]
[tex]\color{limegreen}\Large\boxed{\bf 75~lei~ a~ doaua~ persoana}[/tex]
Explicație pas cu pas:
Salutare!
Notam cu:
- a - suma in lei ce o are prima persoana
- b - suma in lei ce o are a doua persoana
1️⃣ [tex]\large \bf a+b = 200~lei[/tex]
2️⃣ [tex]\large\bf a - 20 \% \cdot a = b + 20 \% \cdot a[/tex]
[tex]\large\bf a - \dfrac{\not20}{\not100} \cdot a = b + \dfrac{\not20}{\not100} \cdot a[/tex]
[tex]\large\bf a - \dfrac{1}{5} \cdot a = b + \dfrac{1}{5} \cdot a~~~\bigg|\cdot 5[/tex]
[tex]\large\bf 5a - a = 5b + a[/tex]
[tex]\large\bf 4a = 5b + a[/tex]
[tex]\large\bf 4a-a = 5b[/tex]
[tex]\large\bf 5b = 3a \implies \boxed{\bf b =\dfrac{3a}{5} }[/tex]
[tex]\large\text{\it Inlocuim pe b in prima relatie si vom avea:}[/tex]
[tex]\large\bf a +\dfrac{3a}{5} = 200~~~\bigg|\cdot 5[/tex]
[tex]\large\bf 5a +3a= 1000[/tex]
[tex]\large\bf 8a= 1000~~~~\bigg|:8[/tex]
[tex]\color{orangered}\Large\boxed{\bf a= 125}[/tex]
[tex]\large\bf 125 +b = 200[/tex]
[tex]\large\bf b = 200 -125[/tex]
[tex]\color{limegreen}\Large\boxed{\bf b = 75}[/tex]
[tex]\large \bf Verificare: 125 +75 = 200~(adevarat)[/tex]
==pav38==
