Question

The admission fee at an amusement park is $2.25 for children and $5.60 for adults. On a certainday, 266 people entered the park, and the admission fees collected totaled $1101. How manychildren and how many adults were admitted?number of children equalsnumber of adults equals

Answer 1

We have to calculate how many adults (A) and children (C) were admitted.

We know that the total number of persons, which is the sum of adults and children, was 266, so we can write:

`A+C=266`

We also know that the fees collected were $1101. This is the sum of the adult tickets, which are price times the number of adults, and the children tickets, which are also price times the amount of children.

Then, we can write this as an equation:

`2.25\cdot C+5.60\cdot A=1101`

We have a system of linear equations with two equations and two unknowns.

We can solve it by substitution as:

`A+C=266\Rightarrow A=266-C`
`\begin{gathered} 2.25C+5.60A=1101 \\ 2.25C+5.60(266-C)=1101 \\ 2.25C+1489.6-5.60C=1101 \\ (2.25-5.60)C=1101-1489.6 \\ -3.35C=-388.6 \\ C=(-388.6)/(-3.35) \\ C=116 \end{gathered}`

We can now use the first equation to calculate the number of adults:

`A=266-C=266-116=150`

Answer:

number of children = 116

number of adults = 150