3.15 Question Generator

3.15 Question Generator - Foley, Ian and Harley Eating Pizza
Foley, Ian and Harley are eating pizza.

Foley eats 1 slices of Sausage and Beef pizza, 4 slices of Peperoni pizza and 4 slices of Cheese pizza. He ate 429 calories in total.
Ian eats 5 slices of Sausage and Beef pizza, 6 slices of Peperoni pizza and 5 slices of Cheese pizza. He ate 695 calories in total.
Harley eats 3 slices of Sausage and Beef pizza, 3 slices of Peperoni pizza and 3 slices of Cheese pizza. He ate 396 calories in total.

This information is summarised in the table below.

	Foley	Ian	Harley
Sausage and Beef	1	5	3
Peperoni	4	6	3
Cheese	4	5	3
Total calories	429	695	396

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?
Harley wants to make it so that he has eaten the most calories. How many slices of Cheese pizza should he eat to make this happen?
Next time Foley, Ian and Harley get together they eat different types of pizza.
- Foley eats 9 slices of Supreme pizza, 7 slices of Neapolitan pizza and 9 slices of Meat Lovers pizza. He ate 1398 calories in total.
- Ian eats 3 slices of Supreme pizza, 7 slices of Neapolitan pizza and 5 slices of Meat Lovers pizza. He ate 828 calories in total.
- Harley eats 6 slices of Supreme pizza, 7 slices of Neapolitan pizza and 7 slices of Meat Lovers pizza. He ate 1113 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.
- Foley eats 10 slices of Chicken and Mushroom pizza, 10 slices of Meatball pizza and 5 slices of Barbeque Chicken pizza. He ate 930 calories in total.
- Ian eats 3 slices of Chicken and Mushroom pizza, 8 slices of Meatball pizza and 1 slices of Barbeque Chicken pizza. He ate 400 calories in total.
- Harley eats 3 slices of Chicken and Mushroom pizza, 8 slices of Meatball pizza and 1 slices of Barbeque Chicken pizza. He ate 400 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:
   33 calories in a slice Sausage and Beef pizza.
   35 calories in a slice Peperoni pizza.
   64 calories in a slice Cheese pizza.

Part 2:
Harley should eat 8 slices of Cheese pizza to eat the maximum. He will eat 716 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   63 calories in a slice Supreme pizza.
   57 calories in a slice Neapolitan pizza.
   48 calories in a slice Meat Lovers pizza.
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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