Answer:
Number of Unlimited passes sold were 168.
Step-by-step explanation:
Let Number of Unlimited passes sold be x
and Number of entrance-only passes sold be y.
Total number of passes sold =282
Hence,
![x+y=282 \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=x%2By%3D282%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
Also
Cost for unlimited-ride pass = $50
Cost for entrance-only pass = $20
Total Money for one day = $10,680
Hence,
![\$50x+\$20y=\$10,680\\](https://tex.z-dn.net/?f=%5C%2450x%2B%5C%2420y%3D%5C%2410%2C680%5C%5C)
Dividing by 10 on both side we get;
![5x+2y=1068 \ \ \ \ equation \ 2](https://tex.z-dn.net/?f=5x%2B2y%3D1068%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%202)
Now multiplying equation 1 by 2 we get;
![2x+2y=584 \ \ \ \ equation \ 3](https://tex.z-dn.net/?f=2x%2B2y%3D584%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%203)
Now Subtracting equation 3 from equation 2 we get;
![(5x+2y=1068)-(2x+2y=584)\\3x=504\\x=\frac{504}{3}= 168](https://tex.z-dn.net/?f=%285x%2B2y%3D1068%29-%282x%2B2y%3D584%29%5C%5C3x%3D504%5C%5Cx%3D%5Cfrac%7B504%7D%7B3%7D%3D%20168)
x= 168
x+y = 282
168+y =282
y=282-168
y= 114
Hence, Number of Unlimited passes sold are 168 and Number of entrance-only pass sold is 114.