Question

Numerele a , b , c, d sunt invers proportionale cu 1,(8) ; 0,8 ; 9,(4) si respectiv 8,(3), iar suma lor este 3409. Aflati a , b , c si d .

Answer 1

1,(8)=(18-1)/9=17/9
0,8=8/10=4/5
9,(4)=(94-9)/9=85/9
8,(3)=(83-8)/8=75/9=25/3

k/(17/9)+k/(4/5)+k/(85/9)+k/(25/3)=3409
9k/17+5k/4+9k/85+3k/25=3409
aducem la numitorul comun  2²x5²x17=1700
900k+2125k+180k+204k=3409x1700
3409k=3409x1700
k=1700
a=9k/17=9x1700/17=900
b=5k/4=5x1700/4=2125
c=9k/85=9x1700/85=180
d=3k/25=3x1700/25=204