Question

Aflati
numerele a, b, c, stiind ca:                                                                                                    

b : a = 3 r
4;                                                                                                                                    

c : b = 2 r
5;                                                                                                                                   
 
c – b =27.

Answer 1

c=27+b

(27+b):b=2 r5
27+b=2b+5
27-5=2b-b
22=b

c-22=27, c=27+22, c=49

22:a=3 r4

22=3a+4
22-4=3a
18=3a
18:3=a
6=a

a=6, b=22, c=49

Answer 2

$b\div a=3r 4$ ⇒ $b=3a+4$
$c\div b =2r5$ ⇒ $c=2b+5$
$c-b=27$ ⇒ $c=27+b$

$\left \{ {{c=2b+5} \atop {c=27+b}} \right.$ ⇒ $2b+5=27+b$ ⇒ $2b-b=27-5$ ⇒ $\boxed {b=22}$ ⇒ $\boxed {c=49}$

$22=3a+4$ ⇒ $3a=18$ ⇒ $\boxed {a=6}$