Question

The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 2,000 people entered the park, and the admission fees that were collected totaled $4,750. How many children and how many adults were admitted

Answer 1

700 adults and 1300 children

Explanation:

Let 'C' represent number of children

'A' represent number of adults

->If 2,000 people entered the park, the equation will be

C+A=2000

C=2000-A ->eq(1)

->$1.50 for children and $4.00 for adults.

$1.50C+$4.00A=$4,750

Substituting for C from above.

$1.50(2000-A)+$4.00A= $4,750

$3000-$1.50A+$4.00A=$4,750

$2.50A = $4,750 - $3000

$2.50A=$1750

A= 700

and for children:

eq(1)=>

C=2000-700

C= 1300

Thus, 700 adults and 1300 children were admitted.

Answer 2

In that day 1300 children and 700 adults were admitted.

Explanation:

Since the people who enter the park are either adults or children, the sum of these two types of people must be equal to the total amount that entered the park. So we have:

children + adults = 2000

The total amount collected must be the sum of the people that entered the park multiplied by the ticket fee for each type. We have:

1.5*children + 4*adults = 4750

We now have two equations and two variables so we can solve the system.

children + adults = 2000 equation 1

1.5*children + 4*adults = 4750 equation 2

We can multiply the equation 1 by -1.5 and sum it with the equation 2 to solve for adults, we have:

-1.5*children - 1.5*adults = -3500

1.5*children + 4*adults = 4750

2.5*adults = 1750

adults = 1750/2.5 = 700

To solve for children we apply the found value for adults on the equation 1.

children + 700 = 2000

children = 2000 - 700 = 1300

In that day 1300 children and 700 adults were admitted.