This document summarizes a student's algebra project involving solving a system of linear equations to determine the amount of broccoli and frozen corn needed to meet daily recommended values of calcium and iron. The student shows their work solving the system of equations, finding that 6 servings of broccoli and 14.7 servings of frozen corn are needed. They also reflect on how algebra is important for their career goal of game programming, giving an example of how vectors and matrices are used.

1. Allen Gordon
Algebra
April 27, 2013
Project 1 Parts 1 and 2
Part 1 Gather Nutritional Information
There is 159 mg of calcium and 2.3 mg of iron in 10 ounces of broccoli and 3.3 mg of calcium and .3 mg
of iron in ½ cup of frozen corn. The recommended daily values of calcium and iron are 1000 mg and 18
mg respectively.
Part 2 Construct and solve a system of 2 linear equations
How much broccoli and frozen corn is necessary to reach the minimum recommended daily values of
calcium and iron?
Let x represent the amount of broccoli and y represent the amount of frozen corn needed.
First we need to clear the decimals by adding 10 to both equations:
Next we solve using the elimination by addition method:
First multiple the second equation by -11 to get equivalent equations:
Now we add the 2 equations to get:
To get x we divide both sides by 1337:
Plug in x in the second equation to get y:

2. Solve for y:
You would need to eat about 6 servings of broccoli and about 14.7 servings of frozen corn to amount to
the recommended daily value of calcium and iron. I said almost equal to on both because I rounded up
due to the decimal numbers being so long.
Here are the complete answers without rounding:
X =
Y =
Create a table showing the daily value required for 6 essential nutrients and create a system of
equations without solving to find out the servings that are needed daily.
Calcium Iron Protein Dietary
Fiber
Carbohydrates Sodium
10 oz Broccoli 159 mg 2.3 mg 8000 mg 8500 mg 13600 mg 68.2 mg
4 oz Frozen Corn 3.3 mg .3 mg 2500 mg 2000 mg 17100 mg 2.5 mg
16 oz Roasted
Chicken
21.9 mg 1.8 mg 42200 mg 1400 mg 0 mg 125.6 mg
4 oz White Rice 7.9 mg .9 mg 2100 mg 300 mg 22300 mg .8 mg
4 oz Baked
Potato
22.7 mg 4.3 mg 3700 mg 3200 mg 39900 mg 15.2 mg
1 oz Apple Pie 3.1 mg .1 mg 500 mg 500 mg 9600 mg 75.4 mg
Daily Value 1000 mg 18 mg 50000 mg 25000 mg 30000mg 2400 mg
Let a = broccoli, b = frozen corn, c = roasted chicken, d = white rice, e = baked potato, f = apple pie.

3. Reflection on the importance of Algebra in Computer Programming
Before learning more about Algebra through this class and this project I did not really
understand how Algebra could be useful to me in life. Now that I have an understanding and
appreciation for Algebra I noticed that Algebra is pretty much used in everyday life and I never
realized it. My career focus is game programming which requires a lot of Algebra and not to
mention calculus and trigonometry. An example of when I would need to use Algebra is in
finding vectors which uses the distance formula for a triangular object.
Also since games are created in a 3D atmosphere with artificial intelligence I need to use
not only vectors but matrices as well. For which case I would of course need to use linear algebra
such as the example above. This is needed to be able to make objects move within the game as
the player does something such as hit a ball for a baseball game. In this instance I would need to
use algebra to find the vector for the ball after the ball is hit and the velocity and distance as to
how far and fast the baseball would go within the game.
References
Complete nutritional values for the foods. (n.d.) Retrieved from
http://web.archive.org/web/20100528000129/http://www-
neos.mcs.anl.gov/CaseStudies/dietpy/WebForms/complete_table.html
Netrition.(2011). Reference values for nutritional labeling. Retrieved from
http://www.netrition.com/rdi_page.html