Question

The admission fee at an amusement park is $5.50 for children and 15.00 for adults. On a certain day, 303people entered the park, and the admission fees collected totaled $3,329.00. How many children and howmany adults were admitted?

Answer 1

128 children and 175 adults

Step-by-step explanation

Step 1

Set the equations:

a)

Let x represents the number of children

Let y represents the number of adults

On a certain day, 303 people entered the park,so

`x+y=303\rightarrow equation(1)`

b) total collected: $3,329.00

the fee for a children is 5.50, so the money from the children fee is = x*5.5=5.5x

the fee for a children is 15, so the money from the children fee is = y*15=15y

if the total is $3,329.00

`5.5x+15y=3329\rightarrow equation\text{ (2)}`

Step 2

solve the equations:

a) isolate x in equation (1) and replace in equation(2)

`\begin{gathered} x+y=303\rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=303-y \\ x=303-y\rightarrow equation(3) \end{gathered}`

now,replace in equation (2)

`\begin{gathered} 5.5x+15y=3329\rightarrow equation\text{ (2)} \\ 5.5(303-y)+15y=3329 \\ 1666.5-5.5y+15y=3329 \\ 1666.5+9.5y=3329 \\ \text{subtract 1666.5 in both sides} \\ 1666.5+9.5y-1666.5=3329-1666.5 \\ 9.5y=1662.5 \\ \text{divide both sides by 9.5} \\ (9.5y)/(9.5)=(1662.5)/(9.5) \\ y=175 \end{gathered}`

hence,

the number of admitted adults is 175

b)finally, replace the y value in equation (3)

`\begin{gathered} x=303-y\rightarrow equation(3) \\ x=303-175 \\ x=128 \end{gathered}`

so, the number of admitted children is 128

I hope this helps you