3.15 Question Generator

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

Hasan eats 3 handfuls of Ready Salted chips, 5 handfuls of BBQ chips and 4 handfuls of The Works chips. He ate 869 calories in total.
Jock eats 2 handfuls of Ready Salted chips, 4 handfuls of BBQ chips and 8 handfuls of The Works chips. He ate 1028 calories in total.
Dan eats 9 handfuls of Ready Salted chips, 5 handfuls of BBQ chips and 9 handfuls of The Works chips. He ate 1498 calories in total.

This information is summarised in the table below.

	Hasan	Jock	Dan
Ready Salted	3	2	9
BBQ	5	4	5
The Works	4	8	9
Total calories	869	1028	1498

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?
Hasan wants to make it so that he has eaten the most calories. How many handfuls of The Works chips should he eat to make this happen?
Next time Hasan, Jock and Dan get together they eat different types of chips.
- Hasan eats 1 handfuls of Cheese & Onion chips, 1 handfuls of Chicken chips and 1 handfuls of Tasty Cheese chips. He ate 224 calories in total.
- Jock eats 1 handfuls of Cheese & Onion chips, 1 handfuls of Chicken chips and 5 handfuls of Tasty Cheese chips. He ate 516 calories in total.
- Dan eats 1 handfuls of Cheese & Onion chips, 1 handfuls of Chicken chips and 3 handfuls of Tasty Cheese chips. He ate 370 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 7 handfuls of Sour Cream and Chives chips, 8 handfuls of Smokey Bacon chips and 6 handfuls of Spicy Tomato chips. He ate 1294 calories in total.
- Jock eats 5 handfuls of Sour Cream and Chives chips, 1 handfuls of Smokey Bacon chips and 1 handfuls of Spicy Tomato chips. He ate 493 calories in total.
- Dan eats 7 handfuls of Sour Cream and Chives chips, 8 handfuls of Smokey Bacon chips and 6 handfuls of Spicy Tomato chips. He ate 1294 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:
   44 calories in a handful Ready Salted chips.
   89 calories in a handful BBQ chips.
   73 calories in a handful The Works chips.

Part 2:
Hasan should eat 13 handfuls of The Works chips to eat the maximum. He will eat 1526 calories in total.

Part 3:
Must show equations solved to give a possible solution, eg:
   70 calories in a handful Cheese & Onion chips.
   81 calories in a handful Chicken chips.
   73 calories in a handful Tasty Cheese 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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