Question

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.

Answer 1

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