Tricky Word Problem: Solve It with These Tips | Help with Calculations

[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?

 

[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? )

 

[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

 

[bomba923]

https://www.physicsforums.com/showthread.php?t=92440

Don't double post.
pqnd1987