Question

On a new temperature scale (°Y), water boils at 155.0 °Y and freezes at 0.00 °Y. Calculate the normal human body temperature using this temperature scale. On the Fahrenheit scale, normal human body temperature is 98.6 °F, and water boils at 212.0 °F and freezes at 32.0 °F.
How do you start this and what kind of formulas do you need to solve it? I need a breakdown please

Answer 1

build a ratio. For the first part: \(\dfrac{x}{155^oY}=\dfrac{98.6 °F}{BP\;of\;water\;in\;F}\)

where x is the "normal human body temperature" in Y degrees.

Answer 2

okay wait i didn't know the freezing point of water was 32 F, that changes things. hold on

Answer 3

so: \(\dfrac{x}{155^oY-0^oY}=\dfrac{98.6 °F}{212^oF-32^oF}\)

what you wanna do is basically scale it but building a ratio with the end points

Answer 4

That makes sense!

Answer 5

honestly, no one in science uses Fahrenheit.

Answer 6

true. now if we had to do this in celsius it would be in the same way?

Answer 7

except just different numbers since freezing is 0 in celsius and boiling is 100

Answer 8

now i got x = 84.91 why does that not look correct, or do i have to convert it?

Answer 9

for celsius it would be the same.

Answer 10

i have a website with the answer to this question (just no work shown) and the answer they got is 57.3

Answer 11

i got x=84.90555

and it makes sense, because the F scale is broken up into 180 units
the Y scale is broken into 155 units

so each Y unit (degree) is accounts a larger temperature range than the F degree

Answer 12

what exactly do you mean by 180 units, wouldn't it be 212 units?

Answer 13

in terms of water, no. from the freezing point (32) to the boiling point of water (212) there are (21-32) 180 units.

Answer 14

the fictitious Y scale (just like the celsius scale) take the freezing point of water as zero

Answer 15

Ohh i get it. Hmm so that 57.3 answer is wrong?

Answer 16

yes

Answer 17

you see the attachment? seems reliable since it's from the textbook

Answer 18

i think they messed up.

if you do the same exercise with the celsius scale:

\(\dfrac{x}{155-0}=\dfrac{37}{100-0}\)

x=57.35

Answer 19

Oh wow didn't even think about that. Interesting. thank you very much!

Answer 20

you'd be surprised how many mistakes there are in books (specially in the answers section). no problem !

Answer 21

so would this way of doing it for these sorts of questions always work?

Answer 22

yeah. building ratios is useful in many types of questions, not only this type. It works when you're comparing to things and they're on fixed scales.

Answer 23

two things*

Answer 24

hmm how about for this one then, because i just tried doing it and it's off from the answer given (even though i'm skeptical since there are errors)

Answer 25

i get 29.6

Answer 26

oh wait i actually get it. they added the 40 degrees since it takes 40 degrees to make the scales equal to each other

Answer 27

yeah, i was gonna say, it starts at 40.

Answer 28

and because in the previous problem it started at 0 we didn't have to add or subtract right?

Answer 29

I just thought about that, and it doesn't seem like it.

85-32=53, which is far from the answer.

Answer 30

true. alright then. i'll just have to think more critically with these questions! haha thank you once again

Answer 31

damn, i'm sorry. you did have to.

look: you'd have to subtract 32F scaled to the Y temperature

x/155=32/180 -> x=27.55555

85-27.55555=57.444444

Answer 32

where did you get the 85 from?

Answer 33

from the initial calculation it was 84.91, i rounded for simplicity.

Answer 34

So you have to perform 2 calculations using the same equation and then subtracting the both answers to get the real one?

Answer 35

yeah, it seems like it.

Answer 36

alright, thank you

Answer 37

no problem. sorry about the errors earlier.

Answer 38

not a problem!