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### Number and algebra

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# Mixed up Mixture

### Why do this problem?

This
problem gives practice in converting between a variety of
measures. Don't be put off if your students are not aware of the
meaning of the various reagents: the table can be reconstructed
using knowledge of units alone and a little common sense. Engaging
with a problem containing some unfamiliar elements is a good
general aspect of mathemaical training.
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### Key questions

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Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

The most intimidating part of this question is the scientific
names of the reagents. Encourage students to see past this to the
mathematical structure of
the problem. If it helps, the names of the reagents could be
replaced by letters.

- What is the question asking mathematically?
- Is it possible easily to rule out certain cards from certain positions? What possibilities remain?

You might naturally try Real-life
equations next.

Change the names of the reagents to letters or something
simpler.

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?