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I have five questions (A to E) used in a scorecard, all are currently ranked 0 or 1 meaning if all are answered 1, the total score possible is 5. I want the total of all to be 100 where the increments are mathematically stepped. The sum can be no greater than 100 and question A is much easier to satisfy than B; B is to C and so on. E is the hardest to satisfy and I cannot think how to divide the sum incrementally or multiply up incrementally. I'm thinking the result would be a curve rather than a line.

Playing around I take E at 50 and divide by two for each step. This doesn't total 100.

A 3.125 B 6.25 C 12.5 D 25 E 50

Can someone kindly help me solve this?

Capitalmind
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  • As it stands, your question is ambiguous. Do you want the five scores to form a geometric sequence, as in the example you provided? – Sammy Black Jun 03 '14 at 16:11

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Let's suppose you keep $E = 50$ points, and you want to know what ratio (instead of $1/2$, which you used in your question) will lead to $100$.

So $D$ will be worth $rE$, and $C$ will be worth $r^2E$, and so on, for some ratio $r$.

Then $A + B + C + D + E = (1 + r + r^2 + r^3 + r^4)E$. We want this to be $100$ when $E = 50$, so we want $1 + r + r^2 + r^3 + r^4 = 2$. The reasonable solution to this is about $0.5188$, which is pretty close to $1/2$ on the whole!

So $D = (0.5188)E$, $C = (0.5188)^2E$, and so on.

This is under the assumption that you want a geometric sequence (meaning you get from one to the next by multiplying by a ratio $r$) that totals to $100$ given that $E = 50$, but you should see how to generalize this to geometric sequences with different conditions.

davidlowryduda
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