Respuesta :
Okay, here we have this:
Considering the provided information, we are going to calculate the requested number of adults and childrens, so we obtain the following:
From the information provided we obtain the following system of equations, where x represents the number of adults and y the number of children:
[tex]\begin{gathered} x+y=202 \\ 6x+2y=640 \end{gathered}[/tex]Let's solve by substitution:
We first isolate x from the first equation:
[tex]x=202-y[/tex]Now let's plug into the second equation with what we found for x:
[tex]\begin{gathered} \begin{bmatrix}6\mleft(202-y\mright)+2y=640\end{bmatrix} \\ \begin{bmatrix}1212-4y=640\end{bmatrix} \\ 1212-4y-1212=640-1212 \\ -4y=-572 \\ \frac{-4y}{-4}=\frac{-572}{-4} \\ y=143 \end{gathered}[/tex]And finally let's substitute with the value of y in the equation of x:
[tex]\begin{gathered} x=202-143 \\ x=59 \end{gathered}[/tex]Finally we obtain that they were 59 adults and 143 childrens.
