Simple Word Problem... I think :)

H

HEIF

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Dec 30, 2010
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Hello,

I came across the following problem that I created..... please note that I could get the answer the long way but I am trying to find a formula or equation to solve all problems like this.

Please help!

STARTING WITH $0.00
I have an income of $10,000 an hour
I have “30” stock
To buy “1” stock you must pay $20,000; i.e.: In two hours I will be able to buy “1 stock” for a total of “31 stock”
Every time you purchase “1” stock it increases your hourly income by 525.

Again for example, in two hours I will have 20k and be able to buy “1” stock, bringing my hourly income up to $10,525. After two more hours I will have “32” stock and an hourly income of $11,050.

If you purchase “1” stock every time you have an additional 20k; how long would it take to get to 200? (We are starting at 30 so I guess it would be the additional 170 stock)

I know I can keep adding 525 and figure it out the hard way, but I am curious as to what a formula for a problem like this would look like and how it would work.


Thank you so much!
 
After 40 hours you have 20 stock plus 10500, So, 21 stock and $500.
After 80 hours, you have 42 stock and $1000.
Hence after 320 hours, 168 stock and $4000. So the anwer is 324 hours.

A formula? Well, after 2n hours youll have n+(525/10000)n stocks, i.e. 10525n/10000.

When does this equal 170? Round up. How many hours then?
 
Thank you for your response; hard to find on internet.

I am missing something you did... your entire post confuses me!

Here is my understanding.

Stock cost 20k a peice (constant)
WE HAVE -- 30 stock and start out at 10k an hour
After two hours I will have 31 stock and 10,525 hourly income
THEN --> After approx 1.90023 hours I will be at 32 stock and 11,050 income/hour.
THEN --> After approx 1.80995 hours I will be at 33 stock and 11,575 income/hour.
THEN --> After approx 1.72786 hours I will be at 34 stock and 12,100 income/hour.

As you can see the increase in stock allows us to gain more hourly income, allowing for more stocks purchased per hour.

And so on.....

Maybe this will explain it a bit better, or maybe I just don't understand the more complicated math.

I appreciate any help.

thanks!
 
I assumed the stock purchase and wage to be discrete. As in, you cannot buy stock after 1.9 hours.

After 2 hours, you will have 20,525 and can buy 20525/20000 stock. This leaves 525/20000 left over.
After 4 hours you have 1 stock and can buy 21050/20000 stock. 1050/20000 left over
After 6 hours you have 2 stock and can buy 21575/20000 stock. 1575/20000 left over.
After 8 hours...

The pattern is that after an even number of hours, 2n, you will have n-1 stock and can purchase (20000+n*525)/20000 stock. That is the same as I wrote earlier. The "left over" will be able to buy an additional stock every 40 hours, since 40*525/20000 = (21000)/20000 > 1.
 
Actually, I just realized my calculation technique is slightly off. You wouldn't be able to use the new 525/mo until a month later, since it hasn't earned you anything initially. And instead of 525n/20000, it should be 1050(n-1)/20000 since 525 is added to your monthly income rather than every two months and can't count the current month as adding earnings.

So after 2 hours, youll have 1 stock with none left over 1+1050*0/20000
After 4 hours youll have 2 stock with 1050 left over, 2+1050*1/20000
After 6 hours youll have 3 stock with 2100 left over, 3+1050*2/20000
After 8 hours youll have 4 stock with 3150 left over, 4+1050*3/20000
After 10 hours youll have 5 stock with 4200 left over, 5+1050*4/20000

At 42 hours, youll have 21 stock and 1050*20/20000 additional earnings from the stock, enough to buy one additional stock. So you'll have 22.

Thus after 2n hours, youll have n+(1050*(n-1))/20000 stock. Compare this with the above list i started.
 
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