x - suma initiala a Alexandrei
[tex]x _{1} [/tex] - suma cheltuita prima data :
13,2 % din x = [tex] \frac{132x}{1000} = \frac{33x}{250} [/tex]
[tex] x_{2} - [/tex] - excursia :
[tex] \frac{2}{5} (x- x_{1} )= \frac{2}{5} (x- \frac{33x}{250} ) =\frac{2*217x}{5*250} = \frac{217x}{5*125} = \frac{217x}{625} [/tex]
[tex] x_{3} - restul[/tex] = 781,20
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[tex]x= x_{1} + x_{2} + x_{3} [/tex] ⇒
⇒[tex]x=\frac{33x}{250} + \frac{217x}{625} + 781,20[/tex] (aducem la acelasi numitor) ⇔ [tex] \frac{1250x}{1250} = \frac{5*33x+2*217x+1250*781,20}{1250} [/tex]
⇒ 1250x = 165x + 434x + 976500 ⇔ 1250x - 599x = 976500 ⇒
⇒ 651x = 976500 ⇒ x = 1500 lei (suma initiala)
[tex] x_{1} = \frac{33}{250} *1500 = 198 [/tex] lei ( cheltuiti prima data )
[tex] x_{2} = \frac{217}{625} * 1500= 520,8[/tex] lei (excursia)
