Question

Un elev cheltuieste 30% dintr-o suma de bani, apoi 4/7 din rest, ramanandu-i 570 lei. Ce suma a avut initial elevul?
Va rog ajutati-ma, URGENT!!!!!

Answer 1

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 $\bf \dfrac{4}{7} \cdot \dfrac{70}{100}\cdot x$ a doua cheltuiala

Restul = 570 lei

$\bf \dfrac{30}{100}\cdot x+\dfrac{4}{7} \cdot \dfrac{70}{100}\cdot x+570=x$

$\bf \dfrac{\not30}{\not100}\cdot x+\dfrac{4}{\not7} \cdot \dfrac{\not70}{\not100}\cdot x+570=x$

$\bf \dfrac{3}{10}\cdot x+\dfrac{4}{1} \cdot \dfrac{1}{10}\cdot x+570=x$

$\bf \dfrac{3}{10}\cdot x+\dfrac{4}{10} \cdot x+570=x\:\:\:|\cdot 10$

$\bf 3 x+4 x+5700=10x$

$\bf 7x+5700=10x$

$\bf 5700=10x-7x$

$\bf 5700=3x\:\:\:|:3$

$\boxed{\bf x = 1900\:lei}$

Raspuns: 1900 lei suma initiala a elevului