SOLUTION: My professor gave the class this problem, "the problem of the day", which is optional to do. I would really like to know how to solve this problem, but dont know how to start it. I

Question 350959: My professor gave the class this problem, "the problem of the day", which is optional to do. I would really like to know how to solve this problem, but dont know how to start it. I have a really hard time with word problems.
Albert goes into a store and says "Lend me as much money as I already have, and i will spend $20.00 in your store." The owner agrees, and Albert spends $20.00. Albert does the same thing at a second, third, and fourth store, with the owner agreeing each time. After this Albert has no money. What is the total debt to the four store owners?

a.)$48.50 b.)$57.75 c.)$61.25 d.)$69.75 e.)$75.00
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Albert goes into a store and says "Lend me as much money as I already have,
and i will spend $20.00 in your store."
The owner agrees, and Albert spends $20.00.
Albert does the same thing at a second, third, and fourth store, with the
owner agreeing each time.
After this Albert has no money.
What is the total debt to the four store owners?
:
Determine how much money, that Albert started out with
x = initial amt
:
First store lends him $x,
2x - 20 = amt he has when enters the 2nd store
:
2nd store lends him (2x-20), he spends 20 therefore
when he leaves the 2nd store he has:
2(2x-20) - 20
4x - 40 - 20
4x - 60 = amt when enters the 3rd store
:
3rd store lends him (4x-60), he spends 20 therfore
2(4x-60) - 20
8x - 120 - 20
8x - 140 = amt when enters the 4th store
:
The 4th store lends him (8x-140), he spends 20, has nothing left, therefore
2(8x-140) - 20 = 0
16x - 280 - 20 = 0
16x - 300 = 0
16x = 300
x =
x = $18.75 is Al's initial amt
:
Total up what each store lent him, using the loan expression for each store:
Store 1: (18.75)
Store 2: 2(18.75) - 20 = $17.50
Store 3: 4(18.75 - 60 = $15
Store 4: 8(18.75 - 140) = $10
:
total debt: 18.75 + 17.50 + 15 + 10 = $61.25
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