3.15 Question Generator

3.15 Question Generator - River, Adam and Tony Eating Pie
River, Adam and Tony are eating pie.

River eats 7 pieces of Chicken and Cranberry pie, 4 pieces of Apple pie and 6 pieces of Mince pie. He ate 724 calories in total.
Adam eats 6 pieces of Chicken and Cranberry pie, 10 pieces of Apple pie and 3 pieces of Mince pie. He ate 929 calories in total.
Tony eats 1 pieces of Chicken and Cranberry pie, 3 pieces of Apple pie and 9 pieces of Mince pie. He ate 548 calories in total.

This information is summarised in the table below.

	River	Adam	Tony
Chicken and Cranberry	7	6	1
Apple	4	10	3
Mince	6	3	9
Total calories	724	929	548

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?
Tony wants to make it so that he has eaten the most calories. How many pieces of Mince pie should he eat to make this happen?
Next time River, Adam and Tony get together they eat different types of pie.
- River eats 3 pieces of Potato Top pie, 5 pieces of Steak pie and 5 pieces of Custard pie. He ate 543 calories in total.
- Adam eats 1 pieces of Potato Top pie, 7 pieces of Steak pie and 5 pieces of Custard pie. He ate 473 calories in total.
- Tony eats 2 pieces of Potato Top pie, 6 pieces of Steak pie and 5 pieces of Custard pie. He ate 508 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.
- River eats 2 pieces of Pumpkin pie, 9 pieces of Butter Chicken pie and 6 pieces of Bacon and Egg pie. He ate 1021 calories in total.
- Adam eats 1 pieces of Pumpkin pie, 7 pieces of Butter Chicken pie and 1 pieces of Bacon and Egg pie. He ate 537 calories in total.
- Tony eats 4 pieces of Pumpkin pie, 18 pieces of Butter Chicken pie and 12 pieces of Bacon and Egg pie. He ate 2042 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:
   38 calories in a piece Chicken and Cranberry pie.
   59 calories in a piece Apple pie.
   37 calories in a piece Mince pie.

Part 2:
Tony should eat 20 pieces of Mince pie to eat the maximum. He will eat 955 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   56 calories in a piece Potato Top pie.
   21 calories in a piece Steak pie.
   54 calories in a piece Custard 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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