Răspuns:
Explicație pas cu pas:
[tex]0,(3) = \frac{3}{9}=\frac{1}{3}\\\\\frac{AB}{AC} = \frac{1}{3}\\\\AC =3*AB\\AC = AB + BC[/tex]
[tex]AB + BC = 3*AB\\BC = 2*AB\\1,5 = 2*AB\\AB = \frac{1,5}{2} = 0,75m[/tex]
[tex]AC = AB + BC = 0,75 + 1,5 = 2,25m[/tex]
--------------------------------------------------------------------------------------------------------------
m(∡BAC) = m(∡CAD) + m(∡BAD)
m(∡CAD) = m(∡BAD) + 20°
m(∡BAC) = 110°
Asadar:
110° = m(∡BAD) + 20° + m(∡BAD) = 2*m(∡BAD) + 20°
2*m(∡BAD) = 110° - 20° = 90°
m(∡BAD) = 90°/2 = 45°
m(∡CAD) = m(∡BAD) + 20° = 45° + 20° = 65°
--------------------------------------------------------------------------------------------------------------
Notam cu x suma initiala
A cheltuit 45 de lei, deci a ramas cu (x-45) lei.
Daca a cheltuit apoi 2/3 din rest, inseamna ca la sfarsit a rams cu 1/3 din rest, deci:
[tex]\frac{1}{3} *(x-45)=25 lei[/tex]
[tex]x-45 = 3*25\\x-45=75\\x=45+75\\x=120lei\\\\[/tex]
