Question

Suma a trei numere naturale este 486. Impartind al doilea numar la primul, se obtine catul 3 si restul 18.Impartind al treilea numar la cel de-al doilea, se obtine catul 2 si restul 12. Sa se afle numerele. 

Answer 1

a+b+c=486
b:a=3 rest 18⇒b=3a+18
c:b=2 rest 12⇒c=2b+12 

 c=2(3a+18)+12=> c= 6a+36+12
c=6a+48

a+3a+18+6a+48=486
10a+66=486
10a=486-66
10a=420
a=420:10
a=42

b=3x42+18
b=144

c=6x42+48
c=300

Verificare : 42+144+300=486

Answer 2

$a+b+c=486 \\ \\ b:a=3 \ rest \ 18 <=> b=3a+18 \\ \\ c:b=2 \ rest \ 12 <=>c=2b+12 \\ <=>c=2(3a+18)+12=6a+36+12 \\ <=>c=6a+48 \\ \\ a+3a+18+6a+48=486 \\ 10a+66=486 \\10a=486-66 \\ 10a=420 \\ \\ \boxed{a=42} \\ \\ b=3*42+18 \\ \boxed{b=144} \\ \\ c=6*42+48 \\ \\ \boxed{c=300}$