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 three 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

Although you didn't include the table, I can see that you can build a system of three equations with three variables.

Let the variables K, E and S be the number of hours Katie, Elizabeth and Siobhan volunteer, respectively, in a week.

Then

Katie volunteers 3 hours more than Elizabeth

1) K = 3 + E

Siobhan volunteers 1 hour less than Elizabeth

2) S = E -1

Over three weeks, the number of hours Katie volunteers is equal to the sum of Elizabeth's and Siobhan's.

3) 3K = 3 (E + S).

Now you can solve the system in many ways. I will show which I think is easiest.

First, simplify #3) dividing both sides by 3 to get

4) K = E + S (this is the same # 3 simplified)

Use # 1 and # 4 to obtain

3 + E = E + S

Subtract E from both sides to get

S = 3.

Now you can subtract # 2 from # 1 to get

K - S = 3 + E - (E -1)
K - S = 3 + 1
K - S = 4
K = S + 4
K = 3 + 4 = 7

Now I will use # 2 to obtain E

S = E - 1
E = S + 1
E = 3 + 1
E = 4.

Now you have all the number of hours:
K = 7
E = 4
S = 3

You can (and should) check that those results match the statements.

Answer 2

Let's say that x represents hours that Elizabeth volunteers over 1 week. Katie volunteers x+3 and Siobhan x-1 hours per week. The equation that arises from condition in text is:
3*(x+3) = 3*(x + x-1)
x+3 = 2*x - 1
2*x - x= 3+1
x=4.

Elizabeth volunteers 7 hours
Katie volunteers 4 hours
Siobhan volunteers 3 hours