Maths problem

[cc100]

Can you solve this teaser thats been bugging me?

"A friend has sent you the recipe for oat biscuits:

2oz(ounce) flour
2oz butter
7oz roled oats
3oz sugar

Using the info below, calculate the expected amount of fat in 100 grams of finished oat biscuits.

1oz = 28.35 grams

100 grams of butter contains 90gram of fat.

There is no significant amount of fat in flour, sugar or rolled oats."

Now thats a toughie.

[Arneldo]

i havent read the question!

but - it might be - 7! - just a guess lol

[Tanser_Man]

If i wasn't so knackerd i would answer it.

I love maths aswell.

[Sticks]

One batch assuming no losses due to mixture sticking on the pan makes 14oz of which butter is 50% of the total mass.

Convert to metric 14oz x 28.35 = 396.9g

As butter is 50% of the mass, that makes 198.45g of butter used.

Fat content of butter is given as 90g for every 100g of butter, that is therefore 90%

So in a total batch of 396.9g we have 195.45 x 0.9 = 178.605g of fat in a total batch

To scale down we need to calculate what percentage 100g is of the mass of a total batch

X = 100 / 396.9 = 0.252 or 25.2%

Therefore the fat content should be 178.605 x 0.252 = 45.0g of fat per 100g of oat biscuits

[cc100]

Yes, that is spot on!!

You are very clever Sticks.:thumbs: Ive put this to a number of people (Father, brother, cousin etc) and theyve not managed to get it.

[Arneldo]

Aww - i wasnt right lol!

[cc100]

Ive had a thought though:

Im sure butter is not 50% of the mass. Butter is two parts in 14 or approximately 14.28% of the mass - isn't it?

[cc100]

Ive worked it out as:

Percentage of biscuit recipe (and therefore any amount of biscuits) taken-up by butter:
2/(2+2+7+3)*100=14.2857% (to 4 decimal places)

Therefore amount of butter (14.2857%) in 100g of biscuits is:
100*14.2857/100=14.2857g (obviously)

There's 90g of fat in 100g of butter, so in other words, 90% of butter is fat.

Therefore amount of fat (90%) in 14.2857g of butter (and therefore 100g of biscuits) is:
90*14.2857/100=12.8572g / 0.4535oz (to 4 decimal places)

Or put simply: 2/(2+2+7+3)*90

[James]

I got the answer to be 12.86g.

[James]

Yeah, you're right cc100. Just looked at your answer.

Sticks went wrong because only 2 parts out of 14 in the recipe are butter, not 50%.

[Sticks]

Just looking at it again, I discovered I was calculating the rolled oats per 100g :blush:

[Sticks]

revisiting the proportion of butter again and redoing the other calculations, converting to metric etc.

I also get 12.86g/100g as well

It must have been because I was in a hurry when asked to look at this that I made some kind of row transposition error.

[cc100]

Nevermind Sticks, we know you are a clever lad.

I asked on here because I know that you are a Physicist.

Thanks for confirming the answer.

(and you James!)

[sol]

I quit maths after GCSE
I dont intend to ever attempt an equasion again!
God knows how i got a C

[Sticks]

Originally posted by sol
I dont intend to ever attempt an equasion again!

does that include English as well? :laugh:

[sol]

hey! i got a B in English
but i still cant spell :laugh: