3 girls get volunteer hours.

Question

Katie, Elizabeth, and Siobhan voluenteer 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.

Answer 1

 

We know nothing about Elizabeth hours, so that is where you assign the variable.

 

Elizabeth = X

Katie = X+3

Siobhan = X -1

 

Assuming this holds true over 3 weeks,

 

  3(x+3) = 3X + 3(x-1)

 

  3x + 9 = 3x + 3x - 3

 

 3x + 9 = 6x - 3

 

 0 = 6x - 3 - 3x - 9

 

 0 = 3x - 12

 

 12 = 3x 

 

 x=4

 

in one week:

Elizabeth volunteers 4 hours

Katie volunteers 7 hours

Siobhan volunteers 3 hours

 

over three weeks:

 Elizabeth volunteers 12 hours

 Katie volunteers 21 hours

Siobhan voluteers 9 hours

 

21 = 12 + 9, so yes it checks.