Complex math question based on proportions!

[EndlesSuccess]

Hi there, I've been working on a specific question for a very long time now. I was introduced to it by my mathematics teacher and I've taken it home with me. I can't seem to get over it, that is until I figure out the correct answer. I've derived various answers but I'm not sure which one is correct. So here's the question:


To interpret the information given on the label of a product, it is important to determine the base for the percents given on the label. Regulations also require that standard daily nutritional values be used as the basis for all labels. Percent daily values are based on a 2,000 calorie diet. The label can also include the recommended daily intakes that are used as a basis for the 2000 and 2500 calorie diet.

Sample Label
Nutrition Facts
Serving size 1/2 cup (114g)
Servings per container: 4
Amount per serving: 260 calories

................................................% Daily values..............
..................................2000 cal....................... 2500 cal............
Total fat = 13 g............... 20%.............................16.25%.......
Saturated fat = 5g.............25%.............................20%......
Cholesterol = 30mg............10%...............................10%......
Sodium - 660 mg..............28%.................................28%..........
Carbohydrate = 31mg..........11%.............................41.25%......
Dietary fibre = 0g.................0%................................0%........

Based on a daily diet of 2000 calories and 2500 calories, are the recommended daily intakes for Total fat proprtional to the daily calories? If the results are reasonably close, you can say that this statement is true. If this statement is true, find the recommended intake value of Total Fat for 1,600 Calorie diet.


- Now I can't say im an expert in this field, but I do quite a bit of expertise. However, I still seem to struggle with what i presume to be a difficult question. I'm not sure how to proceed, let alone discover the recommended value of total fat for 1,600 calorie diet. If anyone can help out, I would very much appreciate it. I would very much like to thank anyone who is willing to take the time to help me figure out the answer to this question!

 

[stapel]

Hi there, I've been working on a specific question for a very long time now.... I've derived various answers but I'm not sure which one is correct.

Please reply with at least one of your answers, showing how you obtained it. Thank you!

 

[EndlesSuccess]

Please reply with at least one of your answers, showing how you obtained it. Thank you!

Haha, why not. I'm pretty sure this isn't correct but it seemed like I was onto something.

(20/100%)(2000cal) = 400 calories fat
(16.25/100%)(2500cal) = 406.25 calories fat

--> yes, the proportions are reasonably similar.

If every serving of 114g gives 20% total fat to a 2000 cal diet,
100% total fat of a 2000 cal diet would be (13*5) 65 grams.
100% total fat of a 2500 cal diet would be (100/16.25=6.15384615 * 13) 80 grams.
difference between both is 15 grams, therefore we can assume that 100% of a 1500 cal diet would be (65-15) 50 grams, and so on.
for every 500 cal gain/loss in the diet, there is a 15 gram difference.
15g fat/500 cal = 0.03g fat/ 1 cal ---> for every 1 cal gain/lost, there is a 0.03g fat difference..
2000-1600 = 400 cal difference.. *0.03g fat/ cal... = 12g difference between 2000cal and 1600 cal

65g fat - 12g fat = 53g total fat recommended value intake(100%) of 1600 cal diet

(13/53g total fat) x 100% = 24.5283%

 

[EndlesSuccess]

Well give it up...go have a BigMac with fries, then a butterscotch sundae...

It's easier to give up, isnt it.
Unfortunately, I dont eat Big Macs

I am very determined to solve this question, with the help of the wonderful members of this forum I'm sure I can achieve that.

 

[EndlesSuccess]

does no one really know how to solve this question?
cmon.. some help would be really good!

bump

 

[EndlesSuccess]

Have you tried Google?

Here's a site that looks promising:
http://www.fda.gov/food/ingredientspackaginglabeling/labelingnutrition/ucm274593.htm

good thinking Denis
using the website you provided, I found a way to determine the total fat in calories available for each diet..
How did I not think of this earlier..

(20/100%)(2000cal) = 400 calories fat
(16.25/100%)(2500cal) = 406.25 calories fat

Well, this may answer the first part of the question.
Can anyone help me figure out the final answer please?
Thank you very much

 

[stapel]

Based on a daily diet of 2000 calories and 2500 calories, are the recommended daily intakes for Total fat proprtional to the daily calories?

I don't understand this question. Where are you given "the recommended daily intakes for total fat"? What do they mean by "proportional to the daily calories"? They seem to be asking you to compare this one label with some benchmark that they don't provide.

 

[EndlesSuccess]

I don't understand this question. Where are you given "the recommended daily intakes for total fat"? What do they mean by "proportional to the daily calories"? They seem to be asking you to compare this one label with some benchmark that they don't provide.

That's what we have to find out. What is meant by 'recommended daily intake' is the 100% value of 1600 calorie diet.
We're given 20% of the recommended daily intake of 2000 and 2500 calorie diet. The first part asks to find proportionate relationship between both total fat and daily calories. The second part asks to use that information and determine 100% of 1600 calorie diet.

Anyways, I have obtained the answer. 53g of total fat is the recommended daily intake (100%) for 1600 calorie diet. 13g of total fat in a 1600 calorie diet is equal to approximately 24.58% of the total intake.
I've edited my second post in this thread with the answer. This project is due tomorrow and im feeling confident in this answer. Again, I would like to thank Denis for directing me in the right path to discovering the solution. Cheers!

 

[Dale10101]

EndlessSpeculation

Hi there, I've been working on a specific question for a very long time now. I was introduced to it by my mathematics teacher and I've taken it home with me. I can't seem to get over it, that is until I figure out the correct answer. I've derived various answers but I'm not sure which one is correct. So here's the question:


To interpret the information given on the label of a product, it is important to determine the base for the percents given on the label. Regulations also require that standard daily nutritional values be used as the basis for all labels. Percent daily values are based on a 2,000 calorie diet. The label can also include the recommended daily intakes that are used as a basis for the 2000 and 2500 calorie diet.

Sample Label
Nutrition Facts
Serving size 1/2 cup (114g)
Servings per container: 4
Amount per serving: 260 calories

................................................% Daily values..............
..................................2000 cal....................... 2500 cal............
Total fat = 13 g............... 20%.............................16.25%.......
Saturated fat = 5g.............25%.............................20%......
Cholesterol = 30mg............10%...............................10%......
Sodium - 660 mg..............28%.................................28%..........
Carbohydrate = 31mg..........11%.............................41.25%......
Dietary fibre = 0g.................0%................................0%........

Based on a daily diet of 2000 calories and 2500 calories, are the recommended daily intakes for Total fat proprtional to the daily calories? If the results are reasonably close, you can say that this statement is true. If this statement is true, find the recommended intake value of Total Fat for 1,600 Calorie diet.


- Now I can't say im an expert in this field, but I do quite a bit of expertise. However, I still seem to struggle with what i presume to be a difficult question. I'm not sure how to proceed, let alone discover the recommended value of total fat for 1,600 calorie diet. If anyone can help out, I would very much appreciate it. I would very much like to thank anyone who is willing to take the time to help me figure out the answer to this question!

I would have thought that 13 g as 20% means that for a 2000 calorie diet 13g is 20/100 = 1/5 of the fat you should eat total, i.e for a 2000 calorie diet you should not eat more them 65g of fat.

Using that logic the total fat you can consume with a 2500 calories diet would be (2500/2000)(65) = 81.25 g

Checking that against 16.25/100 = 1/6.154, and (6.154)(13g) =80. 80 is pretty close to 81.25 ... so maybe?

(1600/2500)(80) = 51.2 grams for total fat for a 1600 calorie diet, and so 20% would yield .2(51.2) = 10.24g.

Basically if you are going to have a 1600 cal intake you should eat 1600/2000 = 80% as much of everything recommended for a 2000 calorie diet ... I mean since the realtionship between the 2000 and 2500 cal diet is approximately linear.

Since it seems that simple I must be wrong ... and I do note that the quasi-linear relationship does not hold for other items. (Crouched position, hands over ears.).