Notam cu:
a - primul numar
b - al doilea numar
c - al treilea numar
"triplul unui numar" inseamna numarul respectiv × 3
"cu 6 mai mare" inseamna operatie de adunare, adica + 6
[tex]\bf a+b+c = 120[/tex]
[tex]\boxed{\bf b= 6 + 3a}[/tex]
[tex]\bf c = 3 + (a+b)[/tex]
inlocuim pe b in ultima relatie⇒ [tex]\bf c = 3 + a +6 +3a[/tex]⇒[tex]\boxed{\bf c = 4a +9}[/tex]
acum inlocuim pe b si c in suma si il vom afla pe a
[tex]\bf a + 3a +6 + 4a + 9 = 120[/tex]
[tex]\bf 8a + 15 = 120[/tex]
[tex]\bf 8a = 120 -15[/tex]
[tex]\bf 8a = 105[/tex]
[tex]\boxed{\bf a = \dfrac{105}{8}}[/tex]
[tex]\bf b=6+3\cdot \dfrac{105}{8}}[/tex] ⇒ [tex]\bf b=6+ \dfrac{315}{8}}[/tex] ⇒[tex]\bf b=\dfrac{315+6\cdot8}{8}}[/tex] ⇒ [tex]\boxed{\bf b=\dfrac{363}{8}}}[/tex]
[tex]\bf c=4\cdot \dfrac{105}{8}+9[/tex]⇒[tex]\bf c=\not4\cdot \dfrac{105}{\not8}+9[/tex]⇒[tex]\bf c= \dfrac{105}{2}+9[/tex]⇒[tex]\bf c=\dfrac{105+9\cdot2}{2}[/tex]⇒[tex]\boxed{\bf c=\dfrac{123}{2}}[/tex]
Verificare:
[tex]\it \dfrac{105}{8} +\dfrac{363}{8}+\dfrac{123}{2}=[/tex]
[tex]\it \dfrac{105+363}{8} +\dfrac{123}{2}=[/tex]
[tex]\it \dfrac{468}{8} +\dfrac{123}{2}=[/tex]
[tex]\it \dfrac{117}{2} +\dfrac{123}{2}=[/tex]
[tex]\it \dfrac{240}{2}=[/tex]
[tex]\it \dfrac{\not240}{\not2}=\boxed{\bf 200}[/tex] (adevarat)
