Question

Ajutor urgent! dau coroana​

Answer 1

Explicație pas cu pas:

☸ Notam cu:

a, b si c sumele celor trei elevi

$\bf a + b + c = 1452$

a - terminat lucrarea in 64 minute

b - terminat lucrarea in 60 + 12 = 72 minute

c - terminat lucrarea in 60 + 20 = 80 minute

$\bf \big\{a, b, c\big\} ~i~p~ \big\{64, 72, 80\big\} \implies$

$\bf \dfrac{a}{ \dfrac{1}{64} } = \dfrac{b}{\dfrac{1}{72} } = \dfrac{c}{ \dfrac{1}{80} } = k$

$\bf 64a = 72b = 80c = k$

$\bf a = \dfrac{k}{64}$

$\bf b = \dfrac{k}{72}$

$\bf c = \dfrac{k}{80}$

Înlocuim in suma si avem:

$\bf \dfrac{k}{64} + \dfrac{k}{72} + \dfrac{k}{80} = 1452$

$\bf \dfrac{45k + 40k + 36k}{2880} = 1452$

$\bf 121k = 1452 \cdot 2880 \implies \boxed{\bf k = 34560}$

$\bf a = \dfrac{34560}{64} \implies \boxed{\bf a = 540~ lei}$

$\bf b = \dfrac{34560}{72}\implies \boxed{\bf b = 480~lei}$

$\bf c = \dfrac{34560}{80} \implies \boxed{\bf c = 432~lei}$

Bafta multa !