Question

A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses by dollar 3. find the original duration of the tour. (Hint use quadratic equation)

Answer 1

The original duration of the tour is 18 days.

Explanation:

Let

the number of days spent be T

Daily expenses be D

Initially ,

total tour expenses was 360

`D * T=360`

`D = (360)/(T)`-------------(1)

If he extends his tour for 4 days, he has to cut down his daily expenses by dollar 3

`(D + 4) \cdot(T -3) = 360`---------------(2)

Expanding the eqaution(2)

DT-3D + 4T -12 = 360

Substituting the value of D

`((360)/(T))T -3( (360)/(T)) + 4T -12 = 360`

`((360)/(T))T -3( (360)/(T)) + 4T= 360 + 12`

`((360)/(T))T -3( (360)/(T)) + 4T= 372`

`360 - ( (1080)/(T)) + 4T= 372`

`( (1080)/(T)) + 4T= 372 - 360`

`( (1080)/(T)) + 4T= 12`

`1080 + 4T^2= 12T`

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 = (360)/(18)`

D = 20