Question

Three siblings- Kate, Sarah, and Dave- committed themselves to volunteer 160 hours for a homeless charity to build new housing . Dave worked 15 hours more than Kate. Sarah worked 5 hours fewer than Kate. How many hours did each of this siblings volunteer?

Answer 1

Kate worked for 50 hours, Dave worked for 65 hours and Sarah

worked for 45 hours

Step-by-step explanation:

Three siblings- Kate, Sarah, and Dave- committed themselves to

volunteer 160 hours for a homeless charity to build new housing

1. Dave worked 15 hours more than Kate

2. Sarah worked 5 hours fewer than Kate

3. The total hours for them is 160 hours

Assume that Kate worked for x hours

∵ Kate worked for x hours

∵ Dave worked 15 hours more than Kate

∴ Dave worked for x + 15 hours

∵ Sarah worked 5 hours fewer than Kate

∴ Sarah worked x - 5 hours

∵ They worked for 160 hours

- Add the number of worked hours of them and equate the sum

  by 160

∴ x + x + 15 + x - 5 = 160

- Add like terms in the left hand side

∴ 3x + 10 = 160

- Subtract 10 from both sides

∴ 3x = 150

- Divide both sides by 3

∴ x = 50 hours

∵ Kate worked for x hours

∴ Kate worked for 50 hours

∵ Dave worked for x + 15 hours

∴ Dave worked for 50 + 15 = 65 hours

∵ Sarah worked for x - 5 hours

∴ Sarah worked for 50 - 5 = 45 hours

Kate worked for 50 hours, Dave worked for 65 hours and Sarah

worked for 45 hours

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