If 550 represents 0 and 1280 represents 15, a value between 550 and 1280, what value does it represent according to the above?

Question

I am trying to improve my math skills, and I am trying to solve this problem:

I have values that can be in the range between 550 and 1280.

550 -> 0  (minimum value represents zero)
1280 -> 15 (maximum value represents 15)
780 -> ??

What is the mathematical formula to calculate the corresponding value if, for example, the input value for this formula is 780?

excuse my ignorance

Your question is very similar to this one, please read through it carefully: https://math.stackexchange.com/questions/3355027/a-function-or-a-factor-to-scale-a-list-of-real-numbers-from-one-range-to-another/3355071#3355071 — Matti P., Nov 09 '20 at 13:35
This cannot be solved the way it is stated: to the values in the range $(550,1280)$ you can assign any numbers you wish. For everything more precise than that, you need to give requirements. (Do bigger numbers get mapped into bigger numbers, i.e. does your map "grow" between $550$ and $1280$? Does it grow linearly (whatever that means)?) If it is a linear map, then $f(x)=\frac{15-0}{1280-550}(x-550)+0$ is the solution. — , Nov 09 '20 at 13:41
@StinkingBishop is this correct? ((15-0)/1280-550) * (780-550)+0 the result is negative.... — yavg, Nov 09 '20 at 14:19

Book Of Flames · Accepted Answer · 2020-11-09T14:58:49.223

1

See that you are basically "squeezing" the scale from $550$ to $1280$ to $0$ and $15$.
Now note that wherever you squeeze the scale, you can always get to $0$ and $15$ as desired. What I mean to say is, e.g. You mapped the $550$ to $1280$ to $0$ to $730$ scale, by subtracting $550$ from all values in the range. (we just replaced the scale now, not squeezed!)

Now the minimum values are zero, which is our advantage. Now when we squeeze the scale, the minimum does not change. Remap the $0$ to $730$ scale to $0$ and $15$ by multiplying each value in that range by $\frac{15}{730}$.

Hence, $780$ from original scale is remapped to $\frac{(780 - 550)15}{730}$.

edited Nov 09 '20 at 14:58

answered Nov 09 '20 at 13:59

Book Of Flames

1,506

thanks for answering, why 730? – yavg Nov 09 '20 at 14:07
@yavg Because then, we see that the maximum value is $15$, which is what we want! – Book Of Flames Nov 09 '20 at 14:08
Excuse my ignorance, but I don't understand where 730 appears, maybe you were wrong and it's 780? – yavg Nov 09 '20 at 14:09
@yavg No, you see that after subtraction our scale was $0$ to $730$. So, you can see what happens if we multiply $\frac{15}{730}$ to each value in that range (including the maximum, which is then $15$). – Book Of Flames Nov 09 '20 at 14:12

score 1 · Answer 2 · answered Nov 09 '20 at 14:24

$780\rightarrow4.726$.

Indeed the unique way to solve this problem is to assume that the function is linear, similar to the Fahrenheit $ \leftrightarrow $ Celsius conversion. Otherwise there are infinite possible answers and the problem makes no sense.

Setting $y = mx +n$ we see that, if $550\to 0$ then $0=550m+n$ which means $n=-550m$

if $1280\to 15$ then $15=1280m+n$

Plug the $n$-value and get $15=1280m-550m\to m=\frac{3}{146}$

and finally $n = -\frac{825}{73}$

So we get $$y = \frac{3}{146}\,x -\frac{825}{73}$$

For $x=780$ we have $y=\frac{345}{73}\approx 4.726$

Hope this helps

score 0 · Answer 3 · answered Nov 09 '20 at 13:35

0

Hint:

Let $y=ax+b$

If $x=550,y=0\implies 0=550a+b$

If $x=1280,y=15\implies ?$

Can you solve the two simultaneous equations in $a,b?$

answered Nov 09 '20 at 13:35

lab bhattacharjee

274,582

If 550 represents 0 and 1280 represents 15, a value between 550 and 1280, what value does it represent according to the above?

3 Answers3