Ratio and proportion

problem

Six Notes All Nice Ratios

Age

14 to 16

Challenge level

1 out of 3

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.
problem

A Scale for the Solar System

Age

14 to 16

Challenge level

1 out of 3

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?
problem

Punky Fish

Age

14 to 16

Challenge level

1 out of 3

A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?
problem

Mixed Up Mixture

Age

14 to 16

Challenge level

1 out of 3

Can you fill in the mixed up numbers in this dilution calculation?
problem

Meeting Point

Age

14 to 16

Challenge level

1 out of 3

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?
problem

Tennis Club

Age

14 to 16

Challenge level

1 out of 3

Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?
problem

Contact

Age

14 to 16

Challenge level

2 out of 3

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?
problem

Gift of Gems

Age

14 to 16

Challenge level

2 out of 3

Four jewellers share their stock. Can you work out the relative values of their gems?
problem

Burning Down

Age

14 to 16

Challenge level

2 out of 3

One night two candles were lit. Can you work out how long each candle was originally?
problem

Rhombus in Rectangle

Age

14 to 16

Challenge level

2 out of 3

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.