Question

katie, elizabeth and scott volunteer at a hospital in one week. katie volunteers 3 more hours than elizabeth and scott volunteers 1 hour less than katie. in over 3 weeks the number of hours katie volunteers is equal to the sum of elizabeth and scotts volunteer hours in 3 weeks

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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.

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Andy C. answered • 08/16/17

TUTOR 4.9 (27)

Math/Physics Tutor

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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.