3.15 Question Generator

3.15 Question Generator - Uzoma, Jock and TJ Eating Pie
Uzoma, Jock and TJ are eating pie.

Uzoma eats 2 pieces of Custard pie, 10 pieces of Pecan pie and 10 pieces of Chicken and Cranberry pie. He ate 1538 calories in total.
Jock eats 10 pieces of Custard pie, 3 pieces of Pecan pie and 7 pieces of Chicken and Cranberry pie. He ate 1642 calories in total.
TJ eats 3 pieces of Custard pie, 9 pieces of Pecan pie and 7 pieces of Chicken and Cranberry pie. He ate 1319 calories in total.

This information is summarised in the table below.

	Uzoma	Jock	TJ
Custard	2	10	3
Pecan	10	3	9
Chicken and Cranberry	10	7	7
Total calories	1538	1642	1319

You are required to write a report using the information above.
Your report needs to answer the following questions:

How many calories are in each piece of pie?
TJ wants to make it so that he has eaten the most calories. How many pieces of Chicken and Cranberry pie should he eat to make this happen?
Next time Uzoma, Jock and TJ get together they eat different types of pie.
- Uzoma eats 5 pieces of Butter Chicken pie, 5 pieces of Mince and Cheese pie and 1 pieces of Potato Top pie. He ate 836 calories in total.
- Jock eats 3 pieces of Butter Chicken pie, 7 pieces of Mince and Cheese pie and 3 pieces of Potato Top pie. He ate 996 calories in total.
- TJ eats 2 pieces of Butter Chicken pie, 3 pieces of Mince and Cheese pie and 1 pieces of Potato Top pie. He ate 458 calories in total.
Based on this information work out how many calories are in each piece of pie.
A year later the boys were getting together, and the pie they liked had changed.
- Uzoma eats 8 pieces of Steak and Cheese pie, 5 pieces of Mince pie and 10 pieces of Blueberry pie. He ate 1264 calories in total.
- Jock eats 3 pieces of Steak and Cheese pie, 7 pieces of Mince pie and 8 pieces of Blueberry pie. He ate 957 calories in total.
- TJ eats 16 pieces of Steak and Cheese pie, 10 pieces of Mince pie and 20 pieces of Blueberry pie. He ate 2528 calories in total.
If possible, work out how many calories are in each piece of pie. Explain giving geometrical reasons for your answer.

As you write your report, take care to clearly communicate your findings, using appropriate mathematical statements. Include relevant equations and calculations.
The quality of your thinking and how well you link this to the context will determine the overall grade.

Answer:

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Part 1:
Must show equations solved to give:
   89 calories in a piece Custard pie.
   50 calories in a piece Pecan pie.
   86 calories in a piece Chicken and Cranberry pie.

Part 2:
TJ should eat 11 pieces of Chicken and Cranberry pie to eat the maximum. He will eat 1663 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   76 calories in a piece Butter Chicken pie.
   75 calories in a piece Mince and Cheese pie.
   81 calories in a piece Potato Top pie.
Or to give a general solution.

Part 4:
Must show equations to find out that that the planes are parallel so there is no solution

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