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Algebra 1

Interpret a Set of Mathematical Models

Algebra 1Interpret a Set of Mathematical Models
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Step 1 - Examine the following nutrition information for some trail mix ingredients.

Calories per gram (kcal) Protein per gram (g) Sugar per gram (g) Fat per Gram (g) Fiber per Gram (g)
Peanuts 5.36 0.21 0.04 0.46 0.07
Almonds 5.71 0.18 0.21 0.46 0.07
Raisins 3.00 0.03 0.60 0.00 0.05
Chocolate pieces 4.76 0.05 0.67 0.19 0.02
Shredded Coconut 6.67 0.07 0.07 0.67 0.13
Sunflower Seeds 5.50 0.20 0.03 0.47 0.10
Dried Cherries 3.25 0.03 0.68 0.00 0.03
Walnuts 6.43 0.14 0.04 0.61 0.07

Step 2 - Tyler and Jada each designed their own custom trail mix using two of these ingredients. Examine the following inequalities they wrote and graphs they created to represent their constraints.

Tyler Jada
  • x+y>50x+y>50
  • 4.76x+6.67y≤4004.76x+6.67y≤400
  • 0.67x+0.07y<300.67x+0.07y<30
  • x>0x>0
  • y>0y>0
Tyler's graph contains a system of three inequalities graphed on a coordinate plane.
  • w+z>50w+z>50
  • 0.14w+0.03z>40.14w+0.03z>4
  • 0.61w+0z≤150.61w+0z≤15
  • w>0w>0
  • z>0z>0
Jada's graph contains a system of three inequalities graphed on a coordinate plane.

Step 3 - Use the inequalities and graphs to answer questions 1 - 5 about each student's trail mix. Be prepared to explain your reasoning.

  1. Which two ingredients did they choose?
  2. What do their variables represent?
  3. What does each constraint mean?
  4. Which graph represents which constraint?
  5. Name one possible combination of ingredients for their trail mix.
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