Answer:
The original duration of the tour is 18 days.
Step-by-step explanation:
Let
the number of days spent be T
Daily expenses be D
Initially ,
total tour expenses was 360
![D \times T=360](https://tex.z-dn.net/?f=D%20%5Ctimes%20T%3D360)
-------------(1)
If he extends his tour for 4 days, he has to cut down his daily expenses by dollar 3
---------------(2)
Expanding the eqaution(2)
DT-3D + 4T -12 = 360
Substituting the value of D
![(\frac{360}{T})T -3( \frac{360}{T}) + 4T -12 = 360](https://tex.z-dn.net/?f=%28%5Cfrac%7B360%7D%7BT%7D%29T%20-3%28%20%5Cfrac%7B360%7D%7BT%7D%29%20%2B%204T%20-12%20%3D%20360)
![(\frac{360}{T})T -3( \frac{360}{T}) + 4T= 360 + 12](https://tex.z-dn.net/?f=%28%5Cfrac%7B360%7D%7BT%7D%29T%20-3%28%20%5Cfrac%7B360%7D%7BT%7D%29%20%2B%204T%3D%20360%20%2B%2012)
![(\frac{360}{T})T -3( \frac{360}{T}) + 4T= 372](https://tex.z-dn.net/?f=%28%5Cfrac%7B360%7D%7BT%7D%29T%20-3%28%20%5Cfrac%7B360%7D%7BT%7D%29%20%2B%204T%3D%20372)
![360 - ( \frac{1080}{T}) + 4T= 372](https://tex.z-dn.net/?f=360%20-%20%28%20%5Cfrac%7B1080%7D%7BT%7D%29%20%2B%204T%3D%20372)
![( \frac{1080}{T}) + 4T= 372 - 360](https://tex.z-dn.net/?f=%20%28%20%5Cfrac%7B1080%7D%7BT%7D%29%20%2B%204T%3D%20372%20-%20360%20)
![( \frac{1080}{T}) + 4T= 12](https://tex.z-dn.net/?f=%20%28%20%5Cfrac%7B1080%7D%7BT%7D%29%20%2B%204T%3D%2012%20)
![1080 + 4T^2= 12T](https://tex.z-dn.net/?f=%201080%20%2B%204T%5E2%3D%2012T%20)
Solving the quadratic equation we get
T = 18 and T = -15
T is the number of gays and it cannot be negative , hence T is 18
Substituting in equation (1) we get
![D = \frac{360}{18}](https://tex.z-dn.net/?f=D%20%3D%20%5Cfrac%7B360%7D%7B18%7D)
D = 20