Question 322928: This coming Halloween, Tom plans to scare twice as many people as Sam, and Sam plans to scare three times as many people as Roz. In all, they plan to scare at most 2005 people. If no one is scared more than once, at most how many people does Sam plan to scare?
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! To solve this problem, you need to make three different equations with the given information.
First, you know that Tom plans to scare twice as many people as Sam:
t = 2s (t= number of people Tom scares, s= number of people Sam scares)
Second, you know that Sam plans to scare three times as many people as Roz:
s = 3r (r= number of people Roz scares)
Third, you know that they plan to scare at most 2005 people total:
t + s + r = 2005
Now you need to combine all three equations. To do this, you need to have only one variable. Since s is the only variable in all three equations, that is what we want to solve for. So we need to rewrite the second equation in terms of s:
s = 3r is the same as r = s/3
Now plug in the first equation and the rewritten second equation into the third equation and solve for s:
t+s+r=2005
(2s) + s + (s/3) = 2005
3s + (1/3)s = 2005
(9/3)s + (1/3)s = 2005
(10/3)s = 2005
s= 601.5
So at most, Sam plans to scare 601 people (can't have half a person and can't round up or else they would scare more than 2005 in total).
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