Answer:
<u>188 children</u> and <u>145 adults</u> were admitted in the park.
Step-by-step explanation:
Given:
The admission fee at an amusement park is $1.50 for children and $4 for adults.
Total $862 collected on a certain day when 333 people enter the park.
Now, to find the children and adults admitted in the park.
<u><em>Let the number of children admitted be </em></u>
<u><em /></u>
<u><em>And the the number of adults admitted be </em></u>
<u><em /></u>
So, the total people enter the park:
![x+y=333\\\\x=333-y\ \ \ ...(1)](https://tex.z-dn.net/?f=x%2By%3D333%5C%5C%5C%5Cx%3D333-y%5C%20%5C%20%5C%20...%281%29)
Thus, the total amount collected of the admission fee:
![1.50(x)+4(y)=862\\\\](https://tex.z-dn.net/?f=1.50%28x%29%2B4%28y%29%3D862%5C%5C%5C%5C)
Substituting the value of
from equation (1):
![1.50(333-y)+4(y)=862\\\\499.50-1.50y+4y=862\\\\499.50+2.50y=862\\\\Subtracting\ both\ sides\ by\ 499.50\ we\ get:\\\\2.50y=362.50\\\\Dividing\ both\ sides\ by\ 2.50\ we\ get:\\\\y=145.](https://tex.z-dn.net/?f=1.50%28333-y%29%2B4%28y%29%3D862%5C%5C%5C%5C499.50-1.50y%2B4y%3D862%5C%5C%5C%5C499.50%2B2.50y%3D862%5C%5C%5C%5CSubtracting%5C%20both%5C%20sides%5C%20by%5C%20499.50%5C%20we%5C%20get%3A%5C%5C%5C%5C2.50y%3D362.50%5C%5C%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%202.50%5C%20we%5C%20get%3A%5C%5C%5C%5Cy%3D145.)
<u><em>Thus, the number of adults = 145.</em></u>
Now, to get the number of children by substituting the value of
in equation (1) we get:
![x=333-y\\\\x=333-145\\\\x=188.](https://tex.z-dn.net/?f=x%3D333-y%5C%5C%5C%5Cx%3D333-145%5C%5C%5C%5Cx%3D188.)
<u><em>Hence, the number of children = 188.</em></u>
Therefore, 188 children and 145 adults were admitted in the park.