Math Help?

Question

Kevin wants a certain amount of platforms that each have a constant increase in height between the shortest and the tallest platform. He needs to decide on the amount of platforms he will use, the height of the first platform, as well as the difference in height from one platform to the next. Camilla needs to decide on the length of material to cover each platform from the top to bottom, based on Kevin’s decisions (width does not matter). This task is to create two formulas that will calculate the height of the tallest platform and the total length of material in terms of the number of platforms, the height of the first platform, and the difference in height between adjacent platforms.

First correct answer is 10 points.

Answer 1

Call the height of the first platform h and let k be the difference between successive platforms. If there are n platforms, the last one will have a height of
h+(n-1)k
and the total amount of material required will be
nh + k*(n*(n-1)/2)

E-mail me if you want a proof ☺

Kewl?

Doug

Answer 2

The heigh of the first platform is h+k, where k is the difference between adjacent platforms and h is the heigh of the lowest one.

k = (H - h)/(n+1) where H is the heigh of the highest platform and n is the amount of platforms they have to build.

h <-k-> 1<-k-> 2<-k-> 3<-k-> 4<-k-> H

Why n+1? If you build 4 platforms, then you have to divide the distance H-h by 5 (that is n+1 in this case) to find out how much is the difference 1-h.

Ilusion