Question

Fie a,b,c trei numere pozitive, astfel incat a/3=b/4 si b/6=c/5 (bara aceea inseamna fractie)
a) aflati numerele naturale x si y, astfel incat a/9=b/x=c/y
b) aflati ce procent reprezinta numarul cel mai mic din numarul cel mai mare.
c) aflati a,b,c daca : 3a-2b+c=26

Answer 1

a)
a/3=b/4
b/6=c/5 

4a=3b sau 12a=9b
5b=6c sau  10b=12c

a/9=b/x

x=9b/a=12a/a=12

x=12

b/12=c/y

y=12c/b=10b/b=10

y=10

b)
Aplicam regula de 3 simpla:

12...........100%
9................x%

x%=9*100/12=75

x%=75

c)
Sistem de 3 ec. cu 3 nec.:

3a-2b+c=26
4a=3b, a=3b/4
5b=6c, c=5b/6

3(3b/4)-2b+5b/6=26

9b/4-2b+5b/6=26

27b-24b+10b=312

13b=312

b=24

a=3*24/4=18

a=18

c=5*24/6

c=20