3.15 Question Generator

3.15 Question Generator - Jock, Uzoma and Jin Myung Eating Pizza
Jock, Uzoma and Jin Myung are eating pizza.

Jock eats 8 slices of Chicken and Mushroom pizza, 8 slices of Peperoni pizza and 10 slices of Spinach and Feta pizza. He ate 1362 calories in total.
Uzoma eats 8 slices of Chicken and Mushroom pizza, 2 slices of Peperoni pizza and 8 slices of Spinach and Feta pizza. He ate 808 calories in total.
Jin Myung eats 3 slices of Chicken and Mushroom pizza, 9 slices of Peperoni pizza and 1 slices of Spinach and Feta pizza. He ate 775 calories in total.

This information is summarised in the table below.

	Jock	Uzoma	Jin Myung
Chicken and Mushroom	8	8	3
Peperoni	8	2	9
Spinach and Feta	10	8	1
Total calories	1362	808	775

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?
Jin Myung wants to make it so that he has eaten the most calories. How many slices of Spinach and Feta pizza should he eat to make this happen?
Next time Jock, Uzoma and Jin Myung get together they eat different types of pizza.
- Jock eats 7 slices of Supreme pizza, 7 slices of Neapolitan pizza and 9 slices of Meatball pizza. He ate 980 calories in total.
- Uzoma eats 9 slices of Supreme pizza, 5 slices of Neapolitan pizza and 5 slices of Meatball pizza. He ate 812 calories in total.
- Jin Myung eats 8 slices of Supreme pizza, 6 slices of Neapolitan pizza and 7 slices of Meatball pizza. He ate 896 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.
- Jock eats 9 slices of Cheese pizza, 9 slices of Meat Lovers pizza and 3 slices of Hawaiian pizza. He ate 1146 calories in total.
- Uzoma eats 9 slices of Cheese pizza, 3 slices of Meat Lovers pizza and 9 slices of Hawaiian pizza. He ate 1355 calories in total.
- Jin Myung eats 3 slices of Cheese pizza, 2 slices of Meat Lovers pizza and 2 slices of Hawaiian pizza. He ate 408 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:
   22 calories in a slice Chicken and Mushroom pizza.
   72 calories in a slice Peperoni pizza.
   61 calories in a slice Spinach and Feta pizza.

Part 2:
Jin Myung should eat 11 slices of Spinach and Feta pizza to eat the maximum. He will eat 1385 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   43 calories in a slice Supreme pizza.
   43 calories in a slice Neapolitan pizza.
   42 calories in a slice Meatball 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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