bob's bank balance initially was 1024$. he spent 50% of his money every day for 5 days. How much money did he have left after the 5 days ended?

Question

 I have no details of my question. I would just like some help

Answer 1

There are a couple of ways to solve this, so I wonder what topic your class is studying right now to find the best solution.

A brute-force way would be to simply track the days with each day half of the previous. That will get you the right answer but it's probably not what your teacher is looking for.

Day 0 ... 1,024
Day 1 ... 512
...
Day 5 ... What do you get?

 

Another way is to notice that 1024 is 2^10 (2 to the tenth power, or 2x2x2x2x2x2x2x2x2x2 (should be 10 of those).

Each day I am basically dividing my balance in half. You might show day 1 as

1024 x 1/2  ... or 1024/2

 

The next days I divide in half again. 

 

(1024 x 1/2) x 1/2

((1024 x 1/2) x 1/2) x 1/2)

 

There is one 1/2 term for each day, so day 5 will have 1/2 multiplied by itself 5 times, or 1/(2^5)

 

Another way to express this is 1024/2, 1024/(2^2), 1024/(2^3) ... 1024/(2^5).

 

Now remember, 1024 is 2^10, so we have

(2^10)/(2^5)

 

or 

 

2^10
2^5

 

When we have the same base in the numerator and denominator, we can subtract the exponents, and reduce to an integer. Post your answer, or any questions you have getting to this point, and I'll check back.