Question

The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certainday, 377 people entered the park, and the admission fees collected totaled 1028 dollars. How manychildren and how many adults were admitted?

Answer 1

The sum of the children and adults who visited the park that day should be equal to the number of people who entered the park. So if the children are "c" and the adults are "a" we should have:

`a\text{ + c = 377}`

The total amount of fees colected should be equal to the number of children that visited the park multiplied by the entrance fee for children plus the number of adults that visited it multiplied by the fee for adults. Therefore,

`4\cdot a\text{ + 1.5}\cdot c\text{ = 1028}`

We have two equations and two variables forming a system of equations, so we can solve it.

`\left\{ \begin{aligned}a+c=377 \\ 4a+1.5c=1028\end{aligned}\right.`

To solve it we will multiply the first equation by -1.5

`\left\{ \begin{aligned}-1.5a-1.5c=-565.5 \\ 4a+1.5c=1028\end{aligned}\right.`

We now need to sum the expressions.

`\begin{gathered} 4a\text{ -1.5a + 1.5c -1.5c = 1028 -565.5} \\ 2.5a\text{ = 462.5} \\ a\text{ = }(462.5)/(2.5)\text{ = }185 \end{gathered}`

To find the value of children we need to use the value of adults in one of the equations above.

`\begin{gathered} c\text{ = 377 -a} \\ c\text{ = 377 - 185 = }192 \end{gathered}`

There were 192 children visiting that day.