Question

Distanta dintre doua localitati a fost parcursa de un excursionist in patru etape.Stiind ca in prima etapa a parcurs $\frac{1}{4 }$ din drum si inca 20 km, in a doua etapa  $\frac{2}{5}$ din rest si inca 15 km , in a treia etapa $\frac{2}{3 }$ din noul rest , fara 10km,si in a patra etapa ultimii 25 km, sa se afle distanta parcursa in fiecare etapa.

Answer 1

x=lungime drum
x/4+20 =  etapa 1
x-(x/4+20)=x-x/4-20=3x/4-20 = rest
(3x/4-20) *2/5 +15 =3x/10-8+15=3x/10+7=etapa 2
3x/4-20-3x/10-7=(15x-6x)/20-27=9x/20-27=rest
(9x/20-27)*2/3-10=3x/10-18-10=3x/10-28=etapa 3
x/4+20+3x/10+7+3x/10-28+25=x
5x/20+6x/20+6x/20+27-28+25=x
17x/20 +24=x
17x+480=20x
3x=480
x=160 km
etapa 1  160 *1/4+20=60 km
rest 160-60=100 km
etapa 2  100 *2/5+15=55 km
rest 100-55=45 km
etapa 3  45 *2/3-10=20 km
rest 45-20=25 km