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Question 609549: Hello. My assignment is to come up with four essential vitamins/minerals and their recommended daily values. Also, four foods that contain each of those vitamins/minerals. Then I have to construct a linear system of equations that determines how much of each item a person would need to consume to achieve the recommended daily value of each nutrient.
For the minerals, I have: Magnesium- 400mg, Potassium-3500mg, Sodium-2400mg, and Zinc-15mg
The foods that I have chosen and calculated are:
1.)4 oz.Chicken: calcium-17.01mg, iron-1.18mg, magnesium-32.89mg, sodium-83.91mg,potassium-290.30mg, & zinc-1.13mg)
2.) 4oz Salmon: calcium-7.94mg, iron-.62mg, mag-35.15mg,sodium-74.84mg, potassium-425.24mg, zinc-.58mg
3.)Whole wheat: calcium-18.20mg, iron-1.75mg, mag-58.24mg,sodium-9.10mg, potassium-123.76mg, zinc-1.04mg
4.)1 cup 2% Milk: calcium-292.80mg, iron-.05mg, mag-26.84mg,sodium-114.68mg, potassium-341.60mg, zinc-1.17mg
Honestly, I have no idea how to begin to create a linear equation for all of these. Hopefully someone can simplify the process for me, or give me an example of a linear equation that I can use to create one for each food
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I think the trick to this one is to count 4oz chicken, 4oz salmon, some unspecified amount of whole wheat, and 1 cup milk, as "servings." Then let  represent the number of required servings of chicken,  represent the number of required servings of salmon, etc.
Now, make yourself a table:
|
Servings |
Magnesium |
Potassium |
Sodium |
Zinc |
| Chicken |
|
32.89 |
290.30 |
83.91 |
1.13 |
| Salmon |
|
35.15 |
425.24 |
74.84 |
0.58 |
| Whole Wheat |
 |
58.24 |
123.76 |
9.1 |
1.04 |
| 2% Milk |
 |
26.84 |
341.60 |
114.68 |
1.17 |
| Requirement |
|
400 |
3500 |
2400 |
15 |
Next note that the amount of magnesium that you would get from servings of chicken would be  mg. So the total amount of magnesium you would get from this chicken/salmon/wheat/milk diet would be:
And you want this to add up to 400mg of magnesium, so:
 .
The others are set up the exact same way, just read down each of the columns in the table to get the numbers you need.
John
My calculator said it, I believe it, that settles it
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