Question

The admission fee at an amusement park is $3.75 for children and $4.80 for adults. On a certainday, 264 people entered the park, and the admission fees collected totaled $1095. How manychildren and how many adults were admitted?number of children equalsnumber of adults equals

Answer 1

Given:

The admission fee at an amusement park is $3.75 for children and $4.80 for adults.

Let the number of children = x

Let the number of adults = y

On a certain day, 264 people entered the park

So, we have the following equation:

$x+y=264\rightarrow(1)$

And, the admission fees collected totaled $1095

so, we have the following equation:

$3.75x+4.8y=1095\rightarrow(2)$

We will solve the equations (1) and (2) to find the values of (x) and (y)

From equation (1):

$x=264-y\rightarrow(3)$

substitute with (x) from equation (3) into equation (1) then solve for (y):

$3.75\cdot(264-y)+4.8y=1095$

so,

$\begin{gathered} 3.75\cdot264-3.75y+4.8y=1095 \\ -3.75y+4.8y=1095-3.75\cdot264 \\ 1.05y=105 \\ y=\frac{105}{1.05}=100 \end{gathered}$

substitute with (y) into equation (3) to find (x):

$x=264-y=264-100=164$

so, the answer will be:

Number of children = 164

Number of adults = 100