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Three siblings sarah, Dave, and Kate - committed themselves to volunteer 155 hours for a homeless charity to build new housing. Kate worked 10 hours more than Sarah. Dave worked 20 hours fewer than Sarah. How many hours did each of these siblings volunteer?



Answer :

MattD
Kate worked 10 hours more than Sarah. Dave worked 20 hours fewer than Sarah.
A total of 155 hours worked.
x --> Sarah
y --> Dave
z --> Kate

[tex]\begin{cases}x+y+z=155\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}x+x-20+x+10=155\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}3x=165|:3\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}x=55\\z=55+10\\y=55-20\end{cases}[/tex]
[tex]\begin{cases}x=55\\z=65\\y=35\end{cases}[/tex]

Now we see that Kate worked 65 hours, Dave worked 35 hours, and Sarah worked 55 hours.
S+D+K=155

K=S+10

D=S-20

--------------------------------

S+(S-20)+(S+10)=155

S+S-20+S+10=155

3S-10=155

3S=165

S=165/3=55

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If S=55,

K=55+10=65

D=55-20=35

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Therefore, Sarah had worked for 55 hours, Kate had worked for 65 hours and Dave had worked for 35 hours.

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