Step-by-step explanation:
ALGEBRA 1
 Lilly S. asked • 08/16/17
3 girls get volunteer hours.
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.
Follow1
Add comment
More
1 Expert Answer
By:
Best
Andy C. answered • 08/16/17
TUTOR 4.9 (27)
Math/Physics Tutor
SEE TUTORS LIKE THIS
 
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.