Explicație pas cu pas:
☸ Notam cu:
a, b si c sumele celor trei elevi
[tex]\bf a + b + c = 1452[/tex]
a - terminat lucrarea in 64 minute
b - terminat lucrarea in 60 + 12 = 72 minute
c - terminat lucrarea in 60 + 20 = 80 minute
[tex]\bf \big\{a, b, c\big\} ~i~p~ \big\{64, 72, 80\big\} \implies[/tex]
[tex]\bf \dfrac{a}{ \dfrac{1}{64} } = \dfrac{b}{\dfrac{1}{72} } = \dfrac{c}{ \dfrac{1}{80} } = k[/tex]
[tex]\bf 64a = 72b = 80c = k[/tex]
[tex]\bf a = \dfrac{k}{64}[/tex]
[tex]\bf b = \dfrac{k}{72}[/tex]
[tex]\bf c = \dfrac{k}{80}[/tex]
Înlocuim in suma si avem:
[tex]\bf \dfrac{k}{64} + \dfrac{k}{72} + \dfrac{k}{80} = 1452[/tex]
[tex]\bf \dfrac{45k + 40k + 36k}{2880} = 1452[/tex]
[tex]\bf 121k = 1452 \cdot 2880 \implies \boxed{\bf k = 34560}[/tex]
[tex]\bf a = \dfrac{34560}{64} \implies \boxed{\bf a = 540~ lei}[/tex]
[tex]\bf b = \dfrac{34560}{72}\implies \boxed{\bf b = 480~lei}[/tex]
[tex]\bf c = \dfrac{34560}{80} \implies \boxed{\bf c = 432~lei}[/tex]
Bafta multa !
