3.15 Question Generator

3.15 Question Generator - Hasan, Jock and River Eating Chips
Hasan, Jock and River are eating chips.

Hasan eats 7 handfuls of Salt and Vinegar chips, 9 handfuls of Sour Cream and Chives chips and 1 handfuls of Smokey Bacon chips. He ate 1007 calories in total.
Jock eats 10 handfuls of Salt and Vinegar chips, 1 handfuls of Sour Cream and Chives chips and 3 handfuls of Smokey Bacon chips. He ate 673 calories in total.
River eats 7 handfuls of Salt and Vinegar chips, 1 handfuls of Sour Cream and Chives chips and 1 handfuls of Smokey Bacon chips. He ate 447 calories in total.

This information is summarised in the table below.

	Hasan	Jock	River
Salt and Vinegar	7	10	7
Sour Cream and Chives	9	1	1
Smokey Bacon	1	3	1
Total calories	1007	673	447

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?
River wants to make it so that he has eaten the most calories. How many handfuls of Smokey Bacon chips should he eat to make this happen?
Next time Hasan, Jock and River get together they eat different types of chips.
- Hasan eats 3 handfuls of The Works chips, 1 handfuls of Tasty Cheese chips and 1 handfuls of BBQ chips. He ate 197 calories in total.
- Jock eats 7 handfuls of The Works chips, 1 handfuls of Tasty Cheese chips and 9 handfuls of BBQ chips. He ate 897 calories in total.
- River eats 5 handfuls of The Works chips, 1 handfuls of Tasty Cheese chips and 5 handfuls of BBQ chips. He ate 547 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.
- Hasan eats 9 handfuls of Spicy Tomato chips, 1 handfuls of Cheese & Onion chips and 9 handfuls of Prawn Cut chips. He ate 1452 calories in total.
- Jock eats 8 handfuls of Spicy Tomato chips, 2 handfuls of Cheese & Onion chips and 7 handfuls of Prawn Cut chips. He ate 1229 calories in total.
- River eats 8 handfuls of Spicy Tomato chips, 2 handfuls of Cheese & Onion chips and 7 handfuls of Prawn Cut chips. He ate 1229 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:
   48 calories in a handful Salt and Vinegar chips.
   70 calories in a handful Sour Cream and Chives chips.
   41 calories in a handful Smokey Bacon chips.

Part 2:
River should eat 15 handfuls of Smokey Bacon chips to eat the maximum. He will eat 1021 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   21 calories in a handful The Works chips.
   57 calories in a handful Tasty Cheese chips.
   77 calories in a handful BBQ 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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