Răspuns: A doua persoana este mai in vârsta
Explicație pas cu pas:
Notam cu
- a - prima persoana
- b - a doua persoana
[tex]\bf ~In~ prezent: \dfrac{a}{b} = \dfrac{6}{7}\implies 7\cdot a = 6\cdot b \implies \boxed{\bf a = 6b:7}~~sau~~\boxed{\bf a = \dfrac{6b}{7}}[/tex]
[tex]\it~~[/tex]
[tex]\bf ~In~ urma ~cu ~6~ani: \dfrac{a-6}{b-6} = \dfrac{5}{6}[/tex]
Înlocuim valoarea lui a in a doua relatie
[tex]\bf \dfrac{\dfrac{6b}{7} -6}{b-6} = \dfrac{5}{6}\implies\dfrac{\dfrac{6b-6\cdot7}{7}}{b-6} = \dfrac{5}{6}\implies \dfrac{\dfrac{6b-42}{7}}{b-6} = \dfrac{5}{6} \implies[/tex]
[tex]\it~~~[/tex]
[tex]\bf \dfrac{6b-42}{7} : \dfrac{b-6}{1} = \dfrac{5}{6}\implies \dfrac{6b-42}{7} \cdot \dfrac{1}{b-6} = \dfrac{5}{6} \implies \dfrac{6b-42}{7\cdot (b-6)} = \dfrac{5}{6}\implies[/tex]
[tex]\bf \implies 6\cdot(6b-42)= 5\cdot 7\cdot (b-6)[/tex]
[tex]\bf 36b-252= 35b-210[/tex]
[tex]\bf 36b= 35b-210 +250[/tex]
[tex]\bf 36b= 35b+42[/tex]
[tex]\bf 36b - 35b=42[/tex]
[tex]\boxed{\boxed{\bf b=42}}[/tex]
[tex]\bf a = 6\cdot 42 :7\implies a =6\cdot 6 \implies \boxed{\boxed{\bf a = 36}}[/tex]
A doua persoana este mai in vârsta
#copaceibrainly
