1)
elizabeth works part-time to pay for college. she has worked for the last 14 days without a day off for a total of 48 hours. depending on her schedule, she either worked for 3 hours a day or 4 hours a day. during the 14 day period, how many days did elizabeth work for 4 hours a day?

Let the number of 3-hour days be x while the number of 4-hour days be y
The number of 3-hour and 4-hour days add up to 14 (x+y=14)
Also 3 hours  times number of 3-hour days plus 4-hours times number of 4-hour days add up tp 48 (3x+4y=48)
That gives us two simultaneous equations: x+y=14
                                                             3x+4y=48
x=14-y
Putting that x equation into the second equation 3(14-y)+4y=48
                                                                      42-3y+4y=48
                                                                      4y-3y=48-42
                                                                      y=6
x+y=14
x=14-6
x=8
Elizabeth worked 8 3-hour days and 6 4-hour days