Answer:
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.