Question

Numerele a si b sunt invers proportionale cu 5 si 8. Daca a+b=26,atunci determinati numerele a si b.

Answer 1

a*5=b*8=k ⇒a=k/5 b=k/8
a+b=26 ⇒ k/5 + k/8 =26 ⇒ 8k/40 + 5k/40 = 26 ⇒ 13k/40=26 ⇒13k=40*26 ⇒
⇒ k= (40*26) /13 ⇒ k= 40*2 ⇒ k=80

a=k/5 ⇒ a=80/5 ⇒ a=16
b=k/8 ⇒ b=80/8 ⇒ b=10