The Fresh Loaf

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Math Percentage Question Seeking Solution

Janetcook's picture
Janetcook

Math Percentage Question Seeking Solution

Okay, when I began baking I didn't expect to have to remember my college algebra but little did I know what was awaiting me.

Question:

I have 150g of starter at 75% hydration.

I want to know what the formula is that I can apply to determine the weight of the flour and the weight of the water included in that 200g.

If I was working with a 100% starter the solution would be a snap.

But with this I have tried applying all the formulas I know and the only way I can come up with an answer is to do my 'hit and miss' method of math....I find a number less than 200 but greater than 100 and multiply it by 75% until I hit upon the correct combination.

I know there has to be a more direct path but when a problem calls for more than one unknown - I am lost.

So far all I can come up with in a way to express this as a formula is: w= (f x 75%):    f + w = 200g therefore (f x 75%) + f = 200g.  I am at a loss because I don't know what 'f' equals to begin with.... When I try to go any further I get helplessly lost...

Anybody have a SIMPLE formula they would like to share with me???? 

Thanks,

Janet

MadAboutB8's picture
MadAboutB8

You can also use baker percentage to work this out.

Say, starter with 75% hydration would be
Flour 100%
water 75%
total 175%

You now want to work out the composition of 150g starter. Take 150 divide by 175 (baker percent) = 0.86

Take 0.86 multiply the flour percentage, which is 100. You have 0.86*100= 86 g. Water then will be 86g x 75%= 64g.

In 150g starter at 75% hydration, there is 86 g flour and 64g water.

Hope that helps.

Sue

Janetcook's picture
Janetcook

Sue,

THANK YOU!!! and my brain thanks you too!!!    No more hit and miss :-)

I hadn't thought of plugging it into baker's percentages this way; I knew there had to be a simple way.  

Your response is now printed and stored in my baking binder for easy access :-)

Take Care,

Janet

 

sam's picture
sam

Say you have 150 grams of starter at 75% hydration and you want to know how much flour+water in grams.

flour = starter-weight / 1 + hydration

flour = 150 / 1 + 0.75

flour = 85.7 grams

Then subtract the flour weight from 150 and that's your water weight (64.3 grams).

 

Janetcook's picture
Janetcook

Thanks for this reply gvs.

A question:  Please explain where you get the numeral '1' from - or what it represents.  

Everything else I do understand and your method is easy too! The '1' is just throwing me....

Take Care,

Janet

yy's picture
yy

You're on the right track with your formula. Don't lose hope :-)

(f x 0.75) + f = 200

you don't know what "f" is because f is the unknown number you are trying to find. This is not a problem though, because you only have one unknown quantity. This makes it easy:

(f x 0.75) + f = 200

rewrite as:

0.75f + f = 200

combine the "f" terms (0.75 + 1):

1.75f=200

divide both sides by 1.75:

f= 114.3 (rounded to the nearest tenth)

this is your flour weight.

 

Notice that 0.75 * 114.3 is about 85.7 grams, which is your water weight.

114.3 + 85.7 = 200 (this step is not necessary but it helps to check your math).

 

 

 

Home Baker's picture
Home Baker

To find water amount in starter at 75% hydration, ask 75% of "what number" plus "what number" yields 150?
.75x + x = 150, [combine terms, solve for x] x = 86, .75(86) = 64, thus 86 g flour and 64 g water in 150 g starter @ 75% hydration.

p.s: You ask above, "Where did the "1" come from?" Another respondent suggests rewriting a formula with whole number preceding decimal figure, a good idea. A "1" is understood to precede each lone variable in formula. For convenience, I was taught not to write the "1" in formula but to include it in the combining variables step. The formula above becomes:
0.75X + 1.0X = 1.75X

In bakers math the "1" always precedes the weight of the flour, making all other ingredients proportional to flour weight. 

Janetcook's picture
Janetcook

Thanks yy and Homebaker for your imput here too.

Now I know why I was confused by math as a kid!  So many ways to get to an answer.  I was always looking for THE way.

Your formulas make it easy.  I didn't realize that I had only 1 unknown....and I like the question of 'what number' plus 

'what number'......helps give my brain words to go with the numbers.

I was a bit proud of myself for being able to construct a formula....at least I had part of it right - my algebra teacher would be proud of me....After 40 years I now have a practical application for what he was trying to teach us :-)

Thanks again for the help!

Take Care,

Janet

jyslouey's picture
jyslouey

Thank you Sue for your super easy method of working out the flour and water composition for simple minds like me.  I'm so glad Janet asked this question as I also had difficulty working this out but was hesitant to ask.   I have one other question and am hoping someone can enlighten me on this.

I have a storage starter which I maintain at a 100% hydration (fed at 1:2:2).   Supposing I have a recipe that calls for a stiffer starter at 75%  or 80% . would I then be able to convert this starter using say 10-12 grm from the storage starter  and feed it at 86f/64w (or feed it twice at 43/32)  or x gr flour/x gr water (for 80% using your method of calculation ) before I use it to bake my bread?  I know I'll end up with slightly more than 150 grm of SD starter (+10 -12 g max) but I can discard this or can this be added back to the storage starter as food  even if the hydration level is different? I reckon 10 grms is so minimal, I doubt if it would affect the storage starter?     Many thanks. 

Judy

ananda's picture
ananda

Hi Janet,

see below:

[100 divided by 175] multiplied by 200 gives flour quantity

[75 divided by 175] multiplied by 200 gives the water quantity

Best wishes

Andy

Janetcook's picture
Janetcook

Hi Andy,

First thing I noticed when I read Sue's response was that is was just like the one you gave me last week on how to figure ingredient amounts out with % listed only.  Was so nice to be able to know exactly what to do because you had already set the foundation for her piece :-)

As Always - Thanks for your input!

Take Care,

Janet