alevel organic chemistry help

**A student investigated the extent of hydrolysis in an old sample of the fat in part (a). 
The carboxylic acid extracted from a 2.78 g sample of this fat (Mr = 806.0) reacted with 24.5 cm3 of a 0.150 mol dm–3 solution of NaOH. 
Calculate the percentage of the fat that had hydrolysed. 
Show your working.
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i dont understand this

Hey! I just found this on a thread from 6 years ago lol:
To do this, you first need to know that you need 3 moles of NaOH to hydrolyse the fat to give 1 mole of sodium salt then you would react it with 1 mole HCl to get a carboxylic acid (remember from CHEM4 when making soap).
Since we now know that the ratio of NaOH to the fat is 3:1, we can start to work out the question. This is what I would do next:

Work out the number of moles of NaOH which is the concentration multiplied by the volume (change this to dm3 by dividing by 1000). Hence
n(NaOH)= 0.0245dm3*0.15=3.68*10^-3 moles

Then work out the moles of the fat that is going to be hydrolysed by dividing the moles of NaOH by 3. Hence
n(hydrolysed fat)=(3.68*10^-3)/3=1.23*10^-3 moles

Then I would work out the number of moles of the old sample of fat from its given mass and its Mr. Hence
n(sample fat)=2.78g/806=3.45*10^-3 moles

Finally to find out the percentage, you would divide n(hydrolsed fat) by n(sample fat) and multiply by 100%. Therefore
percentage=(1.23*10^-3)/(3.45*10^-3)=0.357 which is 35.7%

what was the point of calculating the moles of NaOH???

So when the fat is hydrolysed to form 3 fatty acids and glycerol, do you assume that only one or all three of the fatty acids react with the NaOH solution? Also, is it possible to do this question through directly finding the molar mass of the carboxylic acid? I tried this method but failed.