SOLUTION: a person on tour has 360 us for his daily expenses. if he extends his tour for 4 days , he has to cut down his daily expense by 3 us. find the original duration of the tour.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a person on tour has 360 us for his daily expenses. if he extends his tour for 4 days , he has to cut down his daily expense by 3 us. find the original duration of the tour.      Log On


   

Question 550388: a person on tour has 360 us for his daily expenses. if he extends his tour for 4 days , he has to cut down his daily expense by 3 us. find the original duration of the tour.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
ex: 3 dollars per day for 5 days is 15 dollars equation looks like: 3d=15 3(5)=15 15 being total amount of money
d=daily expense t=amount of days spent
360=dt
360=%28d%2B4%29%28t-3%29
the more word problems you do the easier it is to recognize thes equations straight from the problem
we want to find duration of tour (t) so solve first equation for (d) daily expenses to be able to substitute
360%2Ft=d
use foil method before substitution
360=%28d%2B4%29%28t-3%29foil
360=%28dt%2B4t-3d-12%29add 12 to both sides
372=dt%2B4t-3dsubstitue for (d)
372=%28360%2Ft%29t%2B4t-3%28360%2Ft%29 multiply
372=360%2B4t-1080%2Ftsubtract 360 from both sides
12=4t-1080%2Ftmultiply everything by t
12t=4t%5E2-1080 subtract 12t
0=4t%5E2-12t-1080 take out the 4
0=4%28t%5E2-3-270%29 find two numbers that multiply to get -270 and add to get -3
.
270=2*5*3*3*3 find all prime numbers to easily find the two numbers your looking for
3*5=15
3*3*2=18
15-18=-3
15*-18=-270
.
0=4%28t-18%29%28t%2B15%29
t=18t=-15
t cant be negative so highlight%28t=18%29
to find d:
360%2Ft=d
360%2F18=d
20=d
check
360=%28d%2B4%29%28t-3%29
360=%2820%2B4%29%2818-3%29
360=%2824%29%2815%29
360=%28360%29
correct