Solving a System by Graphing
SCUBA DIVING TRIP
You plan a 7 day trip to go scuba-diving. You visit two places. You estimate that it will cost $275 per day at the Virgin Islands and $400 per day in South Beach. Your total budget for the 7 days is $2300.
How many days should you spend in each location?
EQUATION 1)------------- time spent spent in Virgin Islands = x (days)
-------------------------------time spent in South Beach = y (days)
-------------------------------total vacation time = 7 (days)
EQUATION 2)------------- daily rate in the Virgin Islands = 275 (dollars per day)
-------------------------------time spent in the Virgin Islands = x (days)
------------------------------daily rate in South Beach = 400 (dollars per day)
-------------------------------time spent in South Beach = y (days)
-------------------------------total 7 day budget = 2300 (dollars)
Equation 1)-------------- x + y = 7 ------------ total vacation time
Equation 2) ------------------275x + 400y = 2300 -------------total 7 day budget
Now that you have your equations, put them both in y-interslope form.
Equation 1)------------- y = -x + 7
Equation 2)---- y = -11/16x + 23/4
The lines will intersect at the point (4,3).
Which means that you should plan to spend 4 days in the Virgin Islands and 3 days in Orlando.
