3.15 Question Generator

3.15 Question Generator - Dan, Adam and Jin Myung Eating Pizza
Dan, Adam and Jin Myung are eating pizza.

Dan eats 9 slices of Neapolitan pizza, 4 slices of Chicken and Mushroom pizza and 1 slices of Meat Lovers pizza. He ate 654 calories in total.
Adam eats 8 slices of Neapolitan pizza, 10 slices of Chicken and Mushroom pizza and 3 slices of Meat Lovers pizza. He ate 1084 calories in total.
Jin Myung eats 1 slices of Neapolitan pizza, 7 slices of Chicken and Mushroom pizza and 5 slices of Meat Lovers pizza. He ate 743 calories in total.

This information is summarised in the table below.

	Dan	Adam	Jin Myung
Neapolitan	9	8	1
Chicken and Mushroom	4	10	7
Meat Lovers	1	3	5
Total calories	654	1084	743

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?
Dan wants to make it so that he has eaten the most calories. How many slices of Meat Lovers pizza should he eat to make this happen?
Next time Dan, Adam and Jin Myung get together they eat different types of pizza.
- Dan eats 1 slices of Sausage and Beef pizza, 7 slices of Peperoni pizza and 1 slices of Vegetarian pizza. He ate 405 calories in total.
- Adam eats 3 slices of Sausage and Beef pizza, 3 slices of Peperoni pizza and 5 slices of Vegetarian pizza. He ate 575 calories in total.
- Jin Myung eats 2 slices of Sausage and Beef pizza, 5 slices of Peperoni pizza and 3 slices of Vegetarian pizza. He ate 490 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.
- Dan eats 8 slices of Barbeque Chicken pizza, 8 slices of Beef and Onion pizza and 2 slices of Supreme pizza. He ate 958 calories in total.
- Adam eats 4 slices of Barbeque Chicken pizza, 7 slices of Beef and Onion pizza and 7 slices of Supreme pizza. He ate 950 calories in total.
- Jin Myung eats 16 slices of Barbeque Chicken pizza, 16 slices of Beef and Onion pizza and 4 slices of Supreme pizza. He ate 1916 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:
   40 calories in a slice Neapolitan pizza.
   59 calories in a slice Chicken and Mushroom pizza.
   58 calories in a slice Meat Lovers pizza.

Part 2:
Dan should eat 9 slices of Meat Lovers pizza to eat the maximum. He will eat 1118 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   21 calories in a slice Sausage and Beef pizza.
   44 calories in a slice Peperoni pizza.
   76 calories in a slice Vegetarian 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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