Respuesta :
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:
[tex]x+y=333\rightarrow(1)[/tex]And, the admission fees collected totaled $1843
so, the equation will be:
[tex]4.25x+7.2y=1843\rightarrow(2)[/tex]We will solve the equations (1) and (2)
From equation (1):
[tex]x=333-y\rightarrow(3)[/tex]substitute with (x) from equation (3) into equation (2):
[tex]4.25\cdot(333-y)+7.2y=1843[/tex]solve the equation to find y:
[tex]\begin{gathered} 4.25\cdot333-4.25y+7.2y=1843 \\ -4.25y+7.2y=1843-4.25\cdot333 \\ 2.95y=427.75 \\ y=\frac{427.75}{2.95}=145 \end{gathered}[/tex]Substitute with (y) into equation (3) to find the value of (x):
[tex]x=333-145=188[/tex]So, the answer will be:
The number of children = x = 188
The number of adults = y = 145
