【Rpta.】La mayor cantidad es 700.
[tex]{\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedimiento}}{\hspace{50pt}\above 1.2pt}[/tex]
Recordemos que el reparto proporcional consiste en dividir una parte en cantidades proporcionales de manera directa o inversa.
La repartición que realizaremos en este problema será de manera directamente proporcional, por ello realizamos lo siguiente:
[tex]\mathsf{\dfrac{A}{1} = \dfrac{B}{4} = \dfrac{C}{6} =\dfrac{D}{7} = \boldsymbol{\mathsf{k}}}[/tex]
Siendo A, B, C y D las cantidades repartidas
[tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:A = 1 k}[/tex] [tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:B = 4 k}[/tex] [tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:C = 6k}[/tex] [tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:D = 7k}[/tex]
Al sumar estas tres cantidades nos dará el total, entonces
[tex]\mathsf{\:\:\:\:\:\:\:\:A + B + C+D = Total}\\\\\mathsf{(1k) + (4k) + (6k) +(7k)= 1800}\\\\\mathsf{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:18k = 1800}\\\\\mathsf{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:k = \dfrac{1800}{18}}\\\\\mathsf{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boxed{\boldsymbol{\mathsf{k = 100}}}}[/tex]
Para determinar las cantidades repartidas reemplacemos k en A, B y C
[tex]\mathsf{\blacktriangleright \:\:A=k}\\\\\mathsf{\hspace{10 pt} A=(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{A=100}}}}}[/tex] [tex]\mathsf{\blacktriangleright \:\:B=4k}\\\\\mathsf{\hspace{10 pt} B=4(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{B=400}}}}}[/tex] [tex]\mathsf{\blacktriangleright \:\:C=6k}\\\\\mathsf{\hspace{10 pt} C=6(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{C=600}}}}}[/tex] [tex]\mathsf{\blacktriangleright \:\:D=7k}\\\\\mathsf{\hspace{10 pt} C=7(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{C=700}}}}}[/tex]
[tex]\mathsf{\mathsf{\above 3pt \phantom{aa}\overset{\displaystyle \fbox{I\kern-3pt R}}{}\hspace{4 pt}\displaystyle \fbox{C\kern-6.5pt O}\hspace{4 pt}\overset{\displaystyle\fbox{C\kern-6.5pt G}}{} \hspace{4 pt} \displaystyle \fbox{I\kern-3pt H} \hspace{4pt}\overset{\displaystyle\fbox{I\kern-3pt E}}{} \hspace{4pt}\displaystyle \fbox{I\kern-3pt R} \phantom{aa}} \above 3pt}[/tex]
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【Rpta.】La mayor cantidad es 700.
[tex]{\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedimiento}}{\hspace{50pt}\above 1.2pt}[/tex]
Recordemos que el reparto proporcional consiste en dividir una parte en cantidades proporcionales de manera directa o inversa.
La repartición que realizaremos en este problema será de manera directamente proporcional, por ello realizamos lo siguiente:
[tex]\mathsf{\dfrac{A}{1} = \dfrac{B}{4} = \dfrac{C}{6} =\dfrac{D}{7} = \boldsymbol{\mathsf{k}}}[/tex]
Siendo A, B, C y D las cantidades repartidas
[tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:A = 1 k}[/tex] [tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:B = 4 k}[/tex] [tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:C = 6k}[/tex] [tex]\mathsf{\boldsymbol{\circledcirc \kern-8.7pt +}\:\:\:D = 7k}[/tex]
Al sumar estas tres cantidades nos dará el total, entonces
[tex]\mathsf{\:\:\:\:\:\:\:\:A + B + C+D = Total}\\\\\mathsf{(1k) + (4k) + (6k) +(7k)= 1800}\\\\\mathsf{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:18k = 1800}\\\\\mathsf{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:k = \dfrac{1800}{18}}\\\\\mathsf{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boxed{\boldsymbol{\mathsf{k = 100}}}}[/tex]
Para determinar las cantidades repartidas reemplacemos k en A, B y C
[tex]\mathsf{\blacktriangleright \:\:A=k}\\\\\mathsf{\hspace{10 pt} A=(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{A=100}}}}}[/tex] [tex]\mathsf{\blacktriangleright \:\:B=4k}\\\\\mathsf{\hspace{10 pt} B=4(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{B=400}}}}}[/tex] [tex]\mathsf{\blacktriangleright \:\:C=6k}\\\\\mathsf{\hspace{10 pt} C=6(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{C=600}}}}}[/tex] [tex]\mathsf{\blacktriangleright \:\:D=7k}\\\\\mathsf{\hspace{10 pt} C=7(100)}\\\\\mathsf{\hspace{8 pt}\boxed{\boxed{\boldsymbol{\mathsf{C=700}}}}}[/tex]
[tex]\mathsf{\mathsf{\above 3pt \phantom{aa}\overset{\displaystyle \fbox{I\kern-3pt R}}{}\hspace{4 pt}\displaystyle \fbox{C\kern-6.5pt O}\hspace{4 pt}\overset{\displaystyle\fbox{C\kern-6.5pt G}}{} \hspace{4 pt} \displaystyle \fbox{I\kern-3pt H} \hspace{4pt}\overset{\displaystyle\fbox{I\kern-3pt E}}{} \hspace{4pt}\displaystyle \fbox{I\kern-3pt R} \phantom{aa}} \above 3pt}[/tex]