Question 550388
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=(d+4)(t-3)}}}
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/t=d}}}
use foil method before substitution
{{{360=(d+4)(t-3)}}}foil
{{{360=(dt+4t-3d-12)}}}add 12 to both sides
{{{372=dt+4t-3d}}}substitue for (d)
{{{372=(360/t)t+4t-3(360/t)}}} multiply
{{{372=360+4t-1080/t}}}subtract 360 from both sides
{{{12=4t-1080/t}}}multiply everything by t
{{{12t=4t^2-1080}}} subtract 12t
{{{0=4t^2-12t-1080}}} take out the 4
{{{0=4(t^2-3-270)}}} 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(t-18)(t+15)}}}
{{{t=18}}}{{{t=-15}}}
t cant be negative so {{{highlight(t=18)}}}
to find d:
{{{360/t=d}}}
{{{360/18=d}}}
{{{20=d}}}
check
{{{360=(d+4)(t-3)}}}
{{{360=(20+4)(18-3)}}}
{{{360=(24)(15)}}}
{{{360=(360)}}}
correct