I don't know what problem the onion powder question even wants me to solve.
The question states:
A seasoning blend is 4% onion powder, by mass.
How much pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder?
Because I make more mistakes when working with numbers than with pure symbols (and similar questions come up later) I decided to solve the general problem for any starting percent, target percent, and added percent.
I interpreted the question as "adding X grams of 100% onion powder to a bottle containing 72 grams of 4% onion powder results in the bottle containing 20% onion powder, solve for X", but that interpretation seems to be incorrect as I solve that problem, and get a "correct" answer that is marked as incorrect.
percent = mass / total_mass
given a long list of variables that define the problem
g = starting mass (72g for this question)
o = old percent (4% or 0.04 for this question)
x = added mass (the thing thing I'm trying to solve for)
a = added percent (100% or 1 for this question)
t = target percent (20% or 0.2 for this question)
the equation for concentration becomes:
(go + xa)
/
(g + x)
=
t
which can be rewritten as (as long as g + x is not zero, and negative mass is usually only found in theoretical physics, not kitchens, so neither x nor g should be zero):
go + xa = t(g + x)
which I then tried to solve for x:
go + xa = tg + tx
go + xa - tg = tx
go - tg = tx - xa
go - tg = x(t - a)
(go - tg)/(t - a) = x
and after using the equation with the values for the question I got 14.4,
putting 14.4 back into the volume equation results in:
(0.04*72 + 14.4)
/
(72 + 14.4)
which equals 0.2 according to the khan academy calculator.
but the answer (according to khan academy) is 12, not 14.4.
manually verifying the answer gives the expected value, so I must be misinterpreting the question.
The hints don't help as they don't say how they interpret the question so I don't even know what problem the hints are solving, making it difficult to understand what they are trying to say.
I see the hints also get to 14.4 near the end, but then subtract 2.88 and divide by 0.96, I don't know why.
I tried copy-pasting the text of the hints into this question, but all numbers/equations broke when I did so, making it unreadable.
Please sign in to leave a comment.