Opersoana cheltuieste o suma de bani in 4 zile:in prima zi cheltuieste o trime din suma a doua zi 35% din reste a treia zi 15% din noul rest si in ultima zi restul de 1989 lei. a) ce suma a avut initial persoana? b) ce suma a cheltuit in a II-a zi si a III-a zi?
x-suma de bani 1/3 din x=1/3*x=x/3 -in prima zi x-x/3 aducem la acelasi numitor 3x-x/3=2x/3 -restul 35% din 2x/3=35/100*2x/3=7x/30- a doua zi 2x/3-7x/30 aducem la acelasi numitor 20x-7x/30=13x/30-noul rest 15% din 13x/30=15/100*13x/30=13x/200-a treia zi
x/3+7x/30+13x/200+1989=x aducem la acelasi numitor(600) 200x+140x+39x+1193400=600x 379x-600x=-1193400 -221x=-1193400 x=5400
a) I - 1/3 din x=x/3 rest r1=2/3*x II -35/100*r1 rest r2=65/100*r1 (100-35/100*r1) III -15/100*r2 rest =1989 lei= 85/100*r2 ⇒ r2=100*1989/85=2340 lei 2340 lei=65/100*r1 ⇒ r1=2340*100/65=3600 lei 3600 lei=2/3 *x ⇒ x=3600*3/2=5400 lei (suma initiala) b) II-35/100*3600 lei= 1260 lei III- 15/100*2340 lei= 351 lei verificare 5400= 5400:3+1260+351+1989=1800+1260+351+1989
