Question

Suma a trei nr naturale e 297. Impartind primul nr la al doilea obtinem catul 2 si restul 25, iar impartind primul nr la al treilea obtinem catul 11 si restul 8.
Determinati cele trei nr

Answer 1

a+b+c=297

a:b=2 rest 25=> a= 2b+25=>b=(a-25)/2

a:c=11 rest 8=>a=11c+8=>c=(a-8)/11

a+(a-25)/2+(a-8)/11=297 aduc la acelasi numitor

(22a+11a-275+2a-16)/22=297

(35a-291)/22=297 produsul miezilor=produsul extremilor deci

35a-291=297 ×22

35a-291=6534

35a=6534+291

35a=6825=>a=6825:35=>a=195

b=(a-25)/2=>b=(195-25)/2=>b=170:2=>b=85

c=(a-8)/11=>c=(195-8)/11=>c=187/11=>c=17