Question

A day at the Amusement Park

The admission fee at an amusement park is $9.00 for children and $13.00 for adults. On a
certain day, 251 people entered the park, and the admission fees collected totaled
$2,719.00. How many children and how many adults were admitted?
adults admitted into the park.
There were
children and

Answer 1

115 adults and 136 children were admitted into the amusement park.

Explanation:

We can determine how many children and adults were admitted into the amusement park using a system of equations, where:

• C represents the number of children admitted,
• and A represents the number of adults admitted.

----------------------------------------------------------------------------------------------------------First equation:

Since the admission fees for children and adults were $9.00 and $13.00 respectively and the total admission fees collected was $2719.00, our first equation is given by:

9C + 13A = 2719

Second equation:

Since 251 people entered the park, which includes the children and adults, our second equation is given by:

C + A = 251

Method to Solve: Elimination:

• We can start by multiplying the second equation by -9.

Adding this equation to the first equation will allow us to solve for A and eliminate C since 9C - 9C = 0:

-9(C + A = 251)

-9C - 9A = -2259

Solving for A (i.e., the number of adults admitted):

Now, we can solve for A by adding 9C + 13A = 2719 and -9C - 9A = -2259:

9C + 13A = 2719

+

-9C - 9A = -2259

----------------------------------------------------------------------------------------------------------(9C - 9C) + (13A - 9A) = (2719 - 2259)

(4A = 460) / 4

A = 115

Therefore, 115 adults were admitted into the amusement park.

Solving for C (i.e., the number of children admitted):

Now, we can solve for C by plugging in 115 for A in the first equation (i.e., 9C + 13A = 2719):

9C + 13(115) = 2719

(9C + 1495 = 2719) - 1495

(9C = 1224) / 9

C = 136

Therefore, 136 children were admitted into the amusement park.