# Help with word problem

1. Oct 4, 2005

### pqnd1987

Tricky word problem.

Hi I'm having trouble figuring out how to approach this word problem and wonder if anyone had tips.

Problem:
Just suppose, for the sake of argument, that you have a large block of stone. While staring at this block of stone, it dawns on you that perhaps you should carve it into something. Luckily, you have a hammer and chisel handy.

But it's no ordinary hammer and chisel. Somehow, no matter how hard you hit the chisel, exactly one-half of one percent of the block chips off.

How many times do you have to hit the chisel before the block is less than half of its original size?

2. Oct 4, 2005

### bomba923

Basically, since 0.5% is chipped off each successive strike, you thus retain 99.5% of the block on each successive strike.
*You need to find out how many strikes are needed--->how many 0.5% chips are needed to reduce the block to half of its mass.
*Therefore, letting $n$ be the number of strikes thus far, you will retain $\left( {99.5\% } \right)^n$ of the mass after $n$ strikes.
---To find out the minimal $n$ strikes needed to reduce to less than half the mass will require the inequality:

$$0.995^n < \frac{1}{2} \Rightarrow n \geqslant \left\lceil {\frac{{\log 0.5}}{{\log 0.995}}} \right\rceil \Rightarrow n \geqslant 139$$

*Thus, the minimum quantity of strikes needed is 139.

(since $n \in \mathbb{N} \cup \left\{ 0 \right\}$)
(...tho shouldn't this be in the Homework K-12 section? )

Last edited: Oct 5, 2005
3. Oct 4, 2005

### Kazza_765

After one blow, there is 1* .995 of the block left. After 2 blows there is 2 * .995 of the block left. So after 'n' blows there is .995^n left. So you need to solve: 0.5=0.995^n

4. Oct 5, 2005