✅ Após resolver os cálculos, concluímos que a soma entre o dividendo e o divisor é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf D + d = 254\:\:\:}}\end{gathered}$}[/tex]
Portanto, a opção correta é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf Alternativa\:A\:\:\:}}\end{gathered}$}[/tex]
Sabemos que o algoritmo da divisão pode ser montado da seguinte forma:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf I\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} D = dQ + r\end{gathered}$}[/tex]
Onde:
[tex]\Large\begin{cases} D = Dividendo\\d = Divisor\\Q = Quociente\\r = Resto\end{cases}[/tex]
Sejam os dados:
[tex]\Large\begin{cases} D - d = 224\\Q = 15\\r = 14\\D + d = \:?\end{cases}[/tex]
Sabendo que:
[tex]\Large\displaystyle\text{$\begin{gathered} D - d = 224 \Longrightarrow D = 224 + d\end{gathered}$}[/tex]
Então:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf II\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} D = 224 + d\end{gathered}$}[/tex]
Substituindo "II" em "I", temos:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf III\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} 224 + d = dQ + r\end{gathered}$}[/tex]
Substituindo os valores do quociente "Q" e do resto "r" na equação "III" e, em seguida, resolvendo a equação, temos:
[tex]\Large\displaystyle\text{$\begin{gathered} 224 + d = d\cdot15 + 14\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} 224 + d = 15d + 14\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} d - 15d = 14 - 224\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -14d = -210\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} 14d = 210\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} d = \frac{210}{14}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} d = 15\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \therefore\:\:\:d = 15\end{gathered}$}[/tex]
Agora podemos calcular o valor do dividendo. Para isso, basta inserir o valor de "d" na equação "II", ou seja:
[tex]\Large\displaystyle\text{$\begin{gathered} D = 224 + 15 = 239\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \therefore\:\:\:D = 239\end{gathered}$}[/tex]
Agora devemos realizar a soma entre o dividendo "D" com o divisor "d", isto é:
[tex]\Large\displaystyle\text{$\begin{gathered} D + d = 239 + 15 = 254\end{gathered}$}[/tex]
✅ Portanto, a soma entre o dividendo e o divisor é:
[tex]\Large\displaystyle\text{$\begin{gathered} D + d = 254\end{gathered}$}[/tex]
[tex]\LARGE\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered}$}[/tex]
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