Ratio and Proportion - February 2006, Stage 3&4

Problems

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Cereal Mix

Stage: 3 Challenge Level: Challenge Level:1

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?

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Mixing Paints

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

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Mixing More Paints

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

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A Change in Code

Stage: 4 Challenge Level: Challenge Level:1

There are two sets of numbers. The second is the result of the first after an increase by a constant percentage. How can you find that percentage if one set of numbers is in code?

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Tin Tight

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What's the most efficient proportion for a 1 litre tin of paint?

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Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?