Katie, Elizabeth, and Siobhan volunteer at the hospital. In a week, Katie volunteers 3 hours more than Elizabeth does and Siobhan volunteers 1 hour less than Elizabeth. Over 3 weeks, the number of hours Katie volunteers is equal to the sum of Elizabeth's and Siobhan's volunteer hours in 3 weeks. Complete the table to find out how many hours each person volunteers each week.
Let us assume the number of hours volunteered by Katie = x Number of hours volunteered by Elizabeth = y Number of hours volunteered by Siobhan = z After one week, x = y + 3 z = y - 1 After 3 weeks 3x = 3 (y + z) Dividing both sides by 3, we get x = y + z
Putting the value of x from the first equation in the third equation, we get
x = y + z y + 3 = y + z z = 3
Now putting the value of z in the second equation, we get z = y - 1 3 = y - 1 y = 4 Putting the value of y in the first equation, we get x = y + 3 = 4 + 3 = 7 The number of hours volunteered by Katie = 7 hours Number of hours volunteered by Elizabeth = 4 hours Number of hours volunteered by Siobhan = 3 hours
