a, b, c, d invers proporționale cu numerele 1/2 ,1/3 ,1/5 și respectiv 1/7
[tex]a \cdot \dfrac{1}{2} = b \cdot \dfrac{1}{3} = c \cdot \dfrac{1}{5} = d \cdot \dfrac{1}{7}[/tex]
[tex]a+b+c+d=2023[/tex]
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[tex]\dfrac{a}{2} = \dfrac{b}{3} = \dfrac{c}{5} = \dfrac{d}{7} = \dfrac{a+b+c+d}{2+3+5+7} = \dfrac{2023}{17} = 119[/tex]
(am folosit formula de la rapoarte derivate)
[tex]\dfrac{a}{2} = 119 \implies a = \bf238[/tex]
[tex]\dfrac{b}{3} = 119 \implies b = \bf357[/tex]
[tex]\dfrac{c}{5} = 119 \implies c = \bf595[/tex]
[tex]\dfrac{d}{7} = 119 \implies d = \bf833[/tex]
Proba: 238+357+595+833=2023 (corect!)
