Question

The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day,318 people entered the park, and the admission fees collected totaled 952 dollars. How many children and how many adults were admitted?

Answer 1

To calculate the number of children and adult admitted:

In an amusement park admission fee is 1.5 dollars for children

In an amusement park admission fee is 4 dollars for adults

Let x represent number of Children

Let y represent number of Adult

Step 1: First equation: Children cost $1.50 and Adults cost $4.00. In order to find the amount of money a group of children will cost, we multiply the number of children, x, by 1.5. This is represented by 1.5x. For adults, who cost 4 dollars to enter, we will use 4y. The total amount of money made on the given day was $952. To get this amount, we must add 1.5x and 4y.

`1.5x+4y=952`

Step 2: Second equation: Total amount of people on the given day is 283. To get this number, we must add together x and y, or the number of children and adults.

`x+y=318`

System of equation

`\begin{gathered} 1.5x+4y=952\ldots\ldots(1) \\ x+y=318\ldots\ldots\ldots\text{.}(11) \\ \text{solve using substitution method} \\ \text{from equation (11) , x= 318-y} \end{gathered}`
`\begin{gathered} 1.5(318-y)+4y=952 \\ 477-1.5y+4y=952_{} \\ 2.5y=952-477 \\ 2.5y=475 \\ y=(475)/(2.5) \\ y=190 \end{gathered}`

substitute the value of y in equation 11

`\begin{gathered} x=318-y \\ x=318-190 \\ x=128 \end{gathered}`

Therefore the number of children admitted = 128 , while the number of adult admitted = 190