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.

JaniceHolz

October 20, 2026 14:23

If you add X grams of 100% onion powder to a bottle containing 72 grams of 4% onion powder, the bottle will have X + 72 grams, rather than the 72g required.

Instead, your starting mass of seasoning blend should be 72g - X, so that the sum of the seasoning blend and pure onion powder is 72g. Does this make sense?

(I didn't look at the rest of your set up or calculations.)

Let me know if you get stuck again or also if it works -- I like knowing the outcome :-)

~ Janice (a KA user)

Miro lastname

October 20, 2026 15:40

Thanks, it makes sense.

Although that question should probably make it clear that you're replacing mass inside the bottle with pure onion powder instead of just adding more to the bottle.
It's also weird that the help thing never explained what the question was trying to say and just assumed that you understood it correctly.

> Let me know if you get stuck again or also if it works -- I like knowing the outcome :-)
Using the correct interpretation I got 12, which is correct:

0.04(g - x) + x
/
g
= 0.2

0.04(g - x) + x = 0.2g
0.04g - 0.04x + x = 0.2g
0.04g + 0.96x = 0.2g
0.96x = 0.16g
x = g/6
x = 72/6 = 12

I don't know what problem the onion powder question even wants me to solve.

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