Question 175576: Hi I missed this question at an employment exam. I would like to see how you would solve this: thanks!
Johnny was given x amount of money for his birthday. He spent all of that money in five stores. If he spent half of the money he had plus one dollar at every store, how much money did he originally have?
Found 4 solutions by stanbon, jojo14344, josmiceli, shannonb:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Johnny was given x amount of money for his birthday. He spent all of that money in five stores. If he spent half of the money he had plus one dollar at every store, how much money did he originally have?
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1st store: spend (1/2)x+1
2nd store: spend (1/2)[(1/2)x+1]+1
3rd store: spend (1/2)[(1/2)[(1/2)x+1]+1]+1
4th store: spend (1/2)[(1/2)[(1/2)[(1/2)x+1]+1]+1]+1
5th store: spend (1/2)[(1/2)[(1/2)[(1/2)[(1/2)x+1]+1]+1]+1]+1
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The total amount of spending must = x
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That is a messy equation to solve; I'll leave it to you.
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Cheers,
Stan H.
Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website!
Let  =total money for his b-day
Remember: "Total money=Total expenses"
It follows, Working Eqn, ----->
Now, that "half of his money"---> is not telling us what portion for every store he spend it, right? Anyway it's an expense so we need to add it to the Total Expenses.
Then, the total expenses= half of the money he had,  + $1 for every store.
Continuing,
 combine similar terms
 cross multiply
x=$10 -------->Original Money (ANSWER)
Check via Working Enq:
*If not stisfied, post it again, and somebody might have a better understanding of it.
Thank you,
Jojo
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! At the 1st store, he spent
So, what he had left to spend was
At the 2nd store
He spent half this plus a dollar
So, what he had left to spend was
At the 3rd store
He spent half of this plus a dollar
So, what he had left to spend was
At the 4th store
He spent half of this plus a dollar
So, what he had left to spend was
At the 5th store
He spent half of this plus a dollar
So, what he had left to spend was
But, the problem says he spent all his money and
had nothing left, so
He originally had $62
Now I can check the answer
At the 1st store, he spent
So, what he had left to spend was
At the 2nd store
He spent half this plus a dollar
So, what he had left to spend was
At the 3rd store
He spent half of this plus a dollar
So, what he had left to spend was
At the 4th store
He spent half of this plus a dollar
So, what he had left to spend was
At the 5th store
He spent half of this plus a dollar
So, what he had left to spend was
OK
By the way, were you applying for a job as
a nuclear physicist?
Answer by shannonb(1) (Show Source):
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