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Maths Help please
A flour mill wheat is to be adjusted to moisture content 15% on a dry basis. If the whole grain receivd at the mill is found to contain 11.4% water initially how much water must be added per 100kilo of input grain as received to produce the required water content. The answer is 1.8 kilo to 100 kilo but I cannot work it out. Help please.
Answers
You cant just take 3.6% and use that, because every time you add y kg of water water you are also increasing the overall weight by y kg.
I said suppose the original composition of 100kg is 88.6 kg dry grain and 11.4 kg water.
We want to add y kg of water such that water now accounts for 15% of the overall weight.
New amount of water =...
I said suppose the original composition of 100kg is 88.6 kg dry grain and 11.4 kg water.
We want to add y kg of water such that water now accounts for 15% of the overall weight.
New amount of water =...
07:13 Tue 03rd Aug 2010
Based on my understanding of the question, and assuming all the percentages are based on weight, I get an answer of 4.24 kilo of water needs to be added per 100 kilos of input grain.
What answer do you get yourself? If you show me your calculation answer it might help me see whether the problem could be interpreted in a different way
We'll then try to work it out from there
What answer do you get yourself? If you show me your calculation answer it might help me see whether the problem could be interpreted in a different way
We'll then try to work it out from there
Although I don't have the answer, I find it curious that the difference between the 15% and 11.4% as quoted is 3.6, which is exactly twice the 1.8 answer given by quizbabe. As most questions of this sort often involve adding or subtracting percentages, it's quite a coincidence or is this a clue to the true answer?
You cant just take 3.6% and use that, because every time you add y kg of water water you are also increasing the overall weight by y kg.
I said suppose the original composition of 100kg is 88.6 kg dry grain and 11.4 kg water.
We want to add y kg of water such that water now accounts for 15% of the overall weight.
New total weight = 100+y
New amount of water = 11.4 +y
For the water to be 15% of the overall weight then:
11.4 + y = 0.15 (100 + y)
Expanding brackets:
11.4 +y = 15 + 0.15y
Rearrange:
0.85y =3.6
Solve:
y=3.6/0.85= 4.235
y= 4.235 kg
So you need to add 4.235 kg of water to your initial 100kg of grain received
Have I misunderstood anything?
I said suppose the original composition of 100kg is 88.6 kg dry grain and 11.4 kg water.
We want to add y kg of water such that water now accounts for 15% of the overall weight.
New total weight = 100+y
New amount of water = 11.4 +y
For the water to be 15% of the overall weight then:
11.4 + y = 0.15 (100 + y)
Expanding brackets:
11.4 +y = 15 + 0.15y
Rearrange:
0.85y =3.6
Solve:
y=3.6/0.85= 4.235
y= 4.235 kg
So you need to add 4.235 kg of water to your initial 100kg of grain received
Have I misunderstood anything?
Now I have time to look at this properly. My teacher says the answer is 1.8 to 100 kilo. I tried using your formula but still cannot get to 1.8, however, I have reached 1.8 but still cannot write it down to show how I got it. I said 100 minus 15% = 85. 100 minus 11.4% = 88.6. Deduct 85 from 88.6 = 3.6. Now when you add water you add weight so I divided it by 2 and it is 1.8. This is not the correct way to write it down.
Ah, so the 11.4 % and 15% are being calculated on different bases. It seems the 11.4% is based on the weight of wet grain (combined weight of grain with water =100 kg initially), whereas the 15% figure is calculated as a pecentage of the dry grain weight only (88.6kg). In that case, yes, 1.89 grams of water need to be added to the roiginal 100kg of wet grain.
I need to get into the habit of thinking things through before I go into print and now I'm confused.
As all (weight) percentages of moisture content are '...on a dry basis...' then grain received at 11.4% moisture content is (DRYWEIGHT +11.4%DRYWEIGHT) = 100kg
so DRYWEIGHT of 100kg of received grain is 100kg/1.114 = 89.77kg
A DRYWEIGHT of 89.77kg with a moisture content of 15% weighs 89.77kg x 1.15 = 103.23kg so that the the grain as received (11.4% moisture content) needs 103.23kg - 100kg = 3.23kg of water adding to take it up to a 15% moisture content.
Back to the teacher
As all (weight) percentages of moisture content are '...on a dry basis...' then grain received at 11.4% moisture content is (DRYWEIGHT +11.4%DRYWEIGHT) = 100kg
so DRYWEIGHT of 100kg of received grain is 100kg/1.114 = 89.77kg
A DRYWEIGHT of 89.77kg with a moisture content of 15% weighs 89.77kg x 1.15 = 103.23kg so that the the grain as received (11.4% moisture content) needs 103.23kg - 100kg = 3.23kg of water adding to take it up to a 15% moisture content.
Back to the teacher
Consider the ratio of the original wheat is 88.6/11.4 Kg dry grain to water. The new ratio needs to 85/15 Kg dry grain to water. This means that the weight of grain needs to be reduced by 3.6 Kg and the water increased by 3.6 Kg to keep the total weight at 100 Kg assuming that the grain was totally dry. But as the original grain already contains 11.4 Kg water only half of the weight of water needs to be added otherwise the total weight would exceed 100 Kg
Original grain weighs 88.6 Kg dry grain +11.4 Kg water
New Grain should weigh 85 Kg dry grain +15 Kg water
Add 3.6 Kg water to Original grain new weight would be 103.6 Kg (88.6 +15)
To keep weight at 100 Kg weight of dry grain needs to reduce at same rate as water increases i.e half of the 3.6 Kg = 1.8 Kg
New grain needs to be 86.8 Kg grain + 13.2 Kg water in consist = 15.2 % close enough for most people!!!
Original grain weighs 88.6 Kg dry grain +11.4 Kg water
New Grain should weigh 85 Kg dry grain +15 Kg water
Add 3.6 Kg water to Original grain new weight would be 103.6 Kg (88.6 +15)
To keep weight at 100 Kg weight of dry grain needs to reduce at same rate as water increases i.e half of the 3.6 Kg = 1.8 Kg
New grain needs to be 86.8 Kg grain + 13.2 Kg water in consist = 15.2 % close enough for most people!!!
Consider the ratio of the original wheat is 88.6/11.4 Kg dry grain to water. The new ratio needs to 85/15 Kg dry grain to water. This means that the weight of grain needs to be reduced by 3.6 Kg and the water increased by 3.6 Kg to keep the total weight at 100 Kg assuming that the grain was totally dry. But as the original grain already contains 11.4 Kg water only half of the weight of water needs to be added otherwise the total weight would exceed 100 Kg
Original grain weighs 88.6 Kg dry grain +11.4 Kg water
New Grain should weigh 85 Kg dry grain +15 Kg water
Add 3.6 Kg water to Original grain new weight would be 103.6 Kg (88.6 +15)
To keep weight at 100 Kg weight of dry grain needs to reduce at same rate as water increases i.e half of the 3.6 Kg = 1.8 Kg
New grain needs to be 86.8 Kg grain + 13.2 Kg water in consist = 15.2 % close enough for most people!!!
Original grain weighs 88.6 Kg dry grain +11.4 Kg water
New Grain should weigh 85 Kg dry grain +15 Kg water
Add 3.6 Kg water to Original grain new weight would be 103.6 Kg (88.6 +15)
To keep weight at 100 Kg weight of dry grain needs to reduce at same rate as water increases i.e half of the 3.6 Kg = 1.8 Kg
New grain needs to be 86.8 Kg grain + 13.2 Kg water in consist = 15.2 % close enough for most people!!!
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