3.15 Question Generator

3.15 Question Generator - TJ, Anaru and Foley Eating Chips
TJ, Anaru and Foley are eating chips.

TJ eats 4 handfuls of Prawn Cut chips, 8 handfuls of The Works chips and 5 handfuls of Ready Salted chips. He ate 728 calories in total.
Anaru eats 5 handfuls of Prawn Cut chips, 5 handfuls of The Works chips and 1 handfuls of Ready Salted chips. He ate 344 calories in total.
Foley eats 5 handfuls of Prawn Cut chips, 1 handfuls of The Works chips and 9 handfuls of Ready Salted chips. He ate 916 calories in total.

This information is summarised in the table below.

	TJ	Anaru	Foley
Prawn Cut	4	5	5
The Works	8	5	1
Ready Salted	5	1	9
Total calories	728	344	916

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 handful of chips?
Anaru wants to make it so that he has eaten the most calories. How many handfuls of Ready Salted chips should he eat to make this happen?
Next time TJ, Anaru and Foley get together they eat different types of chips.
- TJ eats 7 handfuls of Chicken chips, 7 handfuls of Tasty Cheese chips and 7 handfuls of Salt and Vinegar chips. He ate 1547 calories in total.
- Anaru eats 3 handfuls of Chicken chips, 5 handfuls of Tasty Cheese chips and 9 handfuls of Salt and Vinegar chips. He ate 1187 calories in total.
- Foley eats 5 handfuls of Chicken chips, 6 handfuls of Tasty Cheese chips and 8 handfuls of Salt and Vinegar chips. He ate 1367 calories in total.
Based on this information work out how many calories are in each handful of chips.
A year later the boys were getting together, and the chips they liked had changed.
- TJ eats 6 handfuls of BBQ chips, 9 handfuls of Cheese & Onion chips and 1 handfuls of Sour Cream and Chives chips. He ate 683 calories in total.
- Anaru eats 3 handfuls of BBQ chips, 10 handfuls of Cheese & Onion chips and 9 handfuls of Sour Cream and Chives chips. He ate 705 calories in total.
- Foley eats 3 handfuls of BBQ chips, 10 handfuls of Cheese & Onion chips and 9 handfuls of Sour Cream and Chives chips. He ate 705 calories in total.
If possible, work out how many calories are in each handful of chips. 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:
   27 calories in a handful Prawn Cut chips.
   25 calories in a handful The Works chips.
   84 calories in a handful Ready Salted chips.

Part 2:
Anaru should eat 8 handfuls of Ready Salted chips to eat the maximum. He will eat 932 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   87 calories in a handful Chicken chips.
   70 calories in a handful Tasty Cheese chips.
   64 calories in a handful Salt and Vinegar chips.
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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