Question

The admission fee at an amusement park is $4.25 for children and $7.20 for adults. On a certainday, 333 people entered the park, and the admission fees collected totaled $1843. How manychildren and how many adults were admitted?

Answer 1

Given:

The admission fee at an amusement park is $4.25 for children and $7.20 for adults.

Let the number of children = x

Let the number of adults = y

On a certain day, 333 people entered the park

so, we have the following equation:

`x+y=333\rightarrow(1)`

And, the admission fees collected totaled $1843

so, the equation will be:

`4.25x+7.2y=1843\rightarrow(2)`

We will solve the equations (1) and (2)

From equation (1):

`x=333-y\rightarrow(3)`

substitute with (x) from equation (3) into equation (2):

`4.25\cdot(333-y)+7.2y=1843`

solve the equation to find y:

`\begin{gathered} 4.25\cdot333-4.25y+7.2y=1843 \\ -4.25y+7.2y=1843-4.25\cdot333 \\ 2.95y=427.75 \\ y=(427.75)/(2.95)=145 \end{gathered}`

Substitute with (y) into equation (3) to find the value of (x):

`x=333-145=188`

So, the answer will be:

The number of children = x = 188

The number of adults = y = 145