3.15 Question Generator

3.15 Question Generator - Anaru, Layne and Hasan Eating Pizza
Anaru, Layne and Hasan are eating pizza.

Anaru eats 6 slices of Sausage and Beef pizza, 6 slices of Margherita pizza and 1 slices of Peperoni pizza. He ate 368 calories in total.
Layne eats 1 slices of Sausage and Beef pizza, 9 slices of Margherita pizza and 2 slices of Peperoni pizza. He ate 431 calories in total.
Hasan eats 5 slices of Sausage and Beef pizza, 7 slices of Margherita pizza and 1 slices of Peperoni pizza. He ate 381 calories in total.

This information is summarised in the table below.

	Anaru	Layne	Hasan
Sausage and Beef	6	1	5
Margherita	6	9	7
Peperoni	1	2	1
Total calories	368	431	381

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 slice of pizza?
Anaru wants to make it so that he has eaten the most calories. How many slices of Peperoni pizza should he eat to make this happen?
Next time Anaru, Layne and Hasan get together they eat different types of pizza.
- Anaru eats 5 slices of Spinach and Feta pizza, 5 slices of Barbeque Chicken pizza and 9 slices of Hawaiian pizza. He ate 1374 calories in total.
- Layne eats 1 slices of Spinach and Feta pizza, 5 slices of Barbeque Chicken pizza and 5 slices of Hawaiian pizza. He ate 834 calories in total.
- Hasan eats 3 slices of Spinach and Feta pizza, 5 slices of Barbeque Chicken pizza and 7 slices of Hawaiian pizza. He ate 1104 calories in total.
Based on this information work out how many calories are in each slice of pizza.
A year later the boys were getting together, and the pizza they liked had changed.
- Anaru eats 7 slices of Supreme pizza, 1 slices of Neapolitan pizza and 9 slices of Meat Lovers pizza. He ate 680 calories in total.
- Layne eats 9 slices of Supreme pizza, 1 slices of Neapolitan pizza and 7 slices of Meat Lovers pizza. He ate 646 calories in total.
- Hasan eats 8 slices of Supreme pizza, 1 slices of Neapolitan pizza and 8 slices of Meat Lovers pizza. He ate 687 calories in total.
If possible, work out how many calories are in each slice of pizza. 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:
   19 calories in a slice Sausage and Beef pizza.
   32 calories in a slice Margherita pizza.
   62 calories in a slice Peperoni pizza.

Part 2:
Anaru should eat 3 slices of Peperoni pizza to eat the maximum. He will eat 492 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   69 calories in a slice Spinach and Feta pizza.
   87 calories in a slice Barbeque Chicken pizza.
   66 calories in a slice Hawaiian pizza.
Or to give a general solution.

Part 4:
Must show equations to find out that that the planes intersect to form a triangular prism so there is no solution

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