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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