Question

Ion parcurge cu autocarul un drum de 3zile.Prima zi parcurge 20% din drum.A doua zi 30% din rest iar a 3-a zi ultimii 560km din drum.
Determinati lungimea drumului parcurs de ion in cele 3zile.

Answer 1

[tex]\text{Notam lungimea drumului cu x.}\\ \dfrac{20}{100}\cdot x+\dfrac{30}{100}\left(x-\dfrac{20}{100}\cdot x\right)+560=x\\ \dfrac{x}{5}+\dfrac{3}{10}\left(x-\dfrac{x}{5}\right)+560=x\\ \dfrac{x}{5}+\dfrac{3}{10}\cdot \dfrac{4x}{5}+560=x\\ \dfrac{x}{5}+\dfrac{6x}{25}+560=x|\cdot 25\\ 5x+6x+14000=25x\\ 11x+14000=25x\\ 14x=14000\Rightarrow \boxed{x=1000\ km}\\ R:\text{Lungimea drumului este de 1000 km.}[/tex]

Answer 2

1)20x/100 =x/5  ;     x -x/5 =5x/5 -x/5 =4x/5   rest
2) 30/100*4x/5 =120x/500 =6x/25
3) 560 km

x/5+6x/25+560 =x    numitor 25
5x +6x +14000 =25x
25x-5x-6x=14000
14x =14000
x =1000 km