Question

The Jurassic Zoo charges $6 for each adult admission and $2 for each child. The total bill for the 202 people from a school trip was $640. How many adults and how many children went to the zoo?

Answer 1

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:

`\begin{gathered} x+y=202 \\ 6x+2y=640 \end{gathered}`

Let's solve by substitution:

We first isolate x from the first equation:

`x=202-y`

Now let's plug into the second equation with what we found for x:

`\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 \\ (-4y)/(-4)=(-572)/(-4) \\ y=143 \end{gathered}`

And finally let's substitute with the value of y in the equation of x:

`\begin{gathered} x=202-143 \\ x=59 \end{gathered}`

Finally we obtain that they were 59 adults and 143 childrens.