Salutare!
Notam cu x suma initaila a elevului
"Cheltuie 30% din suma" 30% · x - cheltuie prima data
→→ rest dupa prima cheltuiala e: 70% · x
"apoi cheltuie 4/7 din rest" asta inseamna [tex]\bf \dfrac{4}{7} \cdot \dfrac{70}{100}\cdot x[/tex] a doua cheltuiala
Restul = 570 lei
[tex]\bf \dfrac{30}{100}\cdot x+\dfrac{4}{7} \cdot \dfrac{70}{100}\cdot x+570=x[/tex]
[tex]\bf \dfrac{\not30}{\not100}\cdot x+\dfrac{4}{\not7} \cdot \dfrac{\not70}{\not100}\cdot x+570=x[/tex]
[tex]\bf \dfrac{3}{10}\cdot x+\dfrac{4}{1} \cdot \dfrac{1}{10}\cdot x+570=x[/tex]
[tex]\bf \dfrac{3}{10}\cdot x+\dfrac{4}{10} \cdot x+570=x\:\:\:|\cdot 10[/tex]
[tex]\bf 3 x+4 x+5700=10x[/tex]
[tex]\bf 7x+5700=10x[/tex]
[tex]\bf 5700=10x-7x[/tex]
[tex]\bf 5700=3x\:\:\:|:3[/tex]
[tex]\boxed{\bf x = 1900\:lei}[/tex]
Raspuns: 1900 lei suma initiala a elevului
