<Student’s name><Professor’s name><Course number>
<The date of the paper>
Part 1. Data collection.
Gather from credible sources the following data:
- The amount of calcium and iron (in milligrams) found in one 10 oz package of broccoli
- The amount of calcium and iron (in milligrams) found in a ½ cup of frozen corn
- The recommended daily values (in milligrams) of calcium and iron
We have found that in 10 oz broccoli there are 116.44 mg of calcium and 2.04 mg of iron.
Also we found, that in 1 cup of frozen corn there are 3.28 mg of calcium and 0.29 mg of iron. Hence, in ½ cup there are 1.64 mg and 0.145 mg respectively.
The dietary supplement fact sheet shows, that the recommended daily values for adults is 1000 mg of calcium and 18 mg of iron (19-50 years old female).
According to the dietary supplement fact sheet we can conclude, that one 10 oz package of broccoli and ½ cup of frozen corn will not allow a person to achieve the minimum levels of calcium and iron for one day. Now we have to construct a system of two equations, to find how much of each food item we need to reach those levels.
Part 2. Building the Meal.
After collecting the data, it should be clear that one 10 oz package of broccoli and one ½ cup of frozen corn will not allow a person to achieve the minimum levels of calcium and iron for one day. To that end, you need to determine how much of each food item you need in order reach those levels. Construct and solve a linear system of two equations that would make that determination.
Let’s the amount of broccoli items is x, and the amount of ½ cups of frozen corn is y. Then, we can write down the equation for calcium necessary level:
116.44∙x+1.64∙y=1000
The same we can do for iron:
2.04∙x+0.145∙y=18
Now we have a system of two equations:
116.44x+1.64y=10002.04x+0.145y=18
Express x from the second equation:
x=18-0.145y2.04
Now substitute in first equation:
116.44(18-0.145y2.04)+1.64y=1000
y=4.1305
x=18-0.145∙4.13052.04=8.5299
Hence, to reach the daily level of iron and calcium we have to eat 8.5299 items of 10 oz broccoli package and 4.1305 of ½ cup of frozen corn. Or, approximately 9 items of broccoli and 2 cups of frozen corn.
Part 3. A More Realistic Meal Plan.
Naturally, people need more than two minerals to survive. Likewise, people eat more than just broccoli and corn. Find four more essential vitamins and minerals and their recommended daily values (in milligrams). Likewise, find four more foods that contain each of the six vitamins and minerals you have listed. Determine that the amount of each nutrient found in one serving of each food.
Using that information, construct but do not solve a linear system of equations that determines how much of each item a person would need to consume to achieve the recommended daily values of each nutrient.
Now we have to find four more foods and four more vitamins. Let’s these foods will be: potato, carrot, peas, beans.
And the vitamins will be protein, lipid, sugar and fiber.
The data is in the table below:
Now, if x1,,x6 is the necessary amount of all these foods, the system has a form:
116.44x1+3.28x2+3.9x3+23.4x4+17x5+273x6=10002.04x1+0.29x2+0.24x3+0.27x4+0.81x5+14.22x6=188.69x1+2.26x2+1.46x3+0.59x4+3.76x5+44.02x6=460.97x1+0.35x2+0.08x3+0.14x4+0.3x5+2.37x6=804.17x1+2.56x2+0.68x3+2.69x4+3.54x5+4.79x6=248.52x1+1.97x2+1.4x3+2.34x4+3.48x5+26.67x6=25
Part 4. Reflection.
Write a statement reflecting on your appreciation for algebra and how it can be applied to areal situation and to your chosen career. Support your statement with examples of applications.
As we can see, algebra is really important tool to solve many real-world problems. In example above we use algebra to find how much foods we have to eat, to save our health. The high school mathematics is only the very beginning of studying a huge knowledge, covering almost all areas of human life. All modern technique and devices are working only through mathematics, all predictions and forecasts are based on mathematical methods, etc. That’s why algebra is a very important thing in our life.
Sources
- http://www.hsph.harvard.edu/nutritionsource/fiber-table/
- http://www.livestrong.com/article/363283-recommended-daily-allowance-of-sugar/
- http://www.webmd.com/food-recipes/protein
- http://www.infoplease.com/ipa/A0922553.html
- http://ods.od.nih.gov/factsheets/Iron-HealthProfessional/
- http://ods.od.nih.gov/factsheets/Calcium-HealthProfessional/
- http://www.stjohnprovidence.org/HealthInfoLib/swarticle.aspx?type=76&id=11094-1
- http://healthlibrary.stjohnprovidence.org/Library/NutritionFacts/76,11911-2
- http://healthlibrary.stjohnprovidence.org/Library/NutritionFacts/76,11757-2
- http://healthlibrary.stjohnprovidence.org/Library/NutritionFacts/76,11813-1
- http://healthlibrary.stjohnprovidence.org/Library/NutritionFacts/76,16040-1
- http://healthlibrary.stjohnprovidence.org/Library/NutritionFacts/76,11365-1
