SOLUTION: My child's Algebra teacher uses problems of the week based on Gary Tsuruda's book "Putting It Together". This week's problem has me stumped. I am educated in math but,... The probl

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Question 380594: My child's Algebra teacher uses problems of the week based on Gary Tsuruda's book "Putting It Together". This week's problem has me stumped. I am educated in math but,... The problem: A man has a bag of coins. He meets three people. The first one gets 1/2 the coins +2. The second gets 1/2 the coins +2. The third gets 1/2 the coins +2. When the man returns home he has two coins in his bag. How many did he start with? I need help with the equation. I tried working backwards, but the answer does not work in the problem. Thanks in advance for any help.
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=number of coins that he started with
First person gets (x/2)+2 leaving x-((x/2)+2)=(x/2)-2
2nd person gets (1/2)((x/2-2)+2=(x/4)+1 leaving (x/2)-2-((x/4)+1)=
(x/2)-2-(x/4)-1=(x/4)-3
3rd person gets(1/2)((x/4)-3)+2 = (x/8)-(3/2)+2=(x/8)+(1/2) leaving 2 coins. So our equation to solve is:
((x/4)-3)-((x/8)+1/2))=2 simplify
(x/4)-3-(x/8)-(1/2)=2
(x/8)-(1/2)=3+2
(x/8)=11/2
x=44---number of coins that he started with
Ck
1st person: (1/2)*44+2=24 leaving 20
2nd person: (1/2)*20+2=12 leaving 8
3rd person: (1/2)*8+2=6 leaving 2
Hope this helps---ptaylor