Question

determinati numerele a,b,c, stiind ca sunt invers proportionale cu 0,(3); 0,5 si 0,25 si ca 6a + 2b - 5c =50

Answer 1

o,(3)=3/9=1/3
0,5=5/10=1/2
0,25=25/100=1/4
invers proportional inseamna  a supra 1 supra 1pe 3
se inmulteste cu inversa ,deci  a/1/1/3=a/1x3/1=3a
tot la fel si celelalte,deci obtinem
3a=2b=4c= ,,k"
3a=k  =>a=k/3
2b=k  =>b=k/2
4c=k  =>c=k/4

avem relatia 6a+2b-5c=50
inlocuim    6k/3+2k/2-5k/4=50
simplificam  2k+k-5k/4=50
numitor comun 4    (8k+4k-5k)4=200/4
inmultim totul cu 4  7k=200  =>k=200/7
a=k/3  =>a=200/7x1/3=200/21
b=k/2  =>b=200/7x1/2=100/7
c=k/4  =>c=200/7x1/4=50/7