Tea or coffee?
All the pupils in a school voted on whether they preferred tea or coffee.
They all chose one or the other.
The winner was coffee by 162 votes. This was three elevenths of the total number of votes.
How many pupils chose tea?
Wheels in wheels
Six circles touch each other as shown. The radius of the middle-sized circle is 1 centimetre.
What is the radius of the large circle?
What is the radius of the small circle?
SOLUTION Tea or coffee? (ages 8 to 12) 216 pupils chose tea. If coffee beat tea by three elevenths, then tea had four elevenths of the votes and coffee had seven elevenths of the votes. If three elevenths is 162, then one eleventh is 54 and four elevenths is 216.
Wheels in wheels (ages 13 to 16) The large circle has radius (C2 + 1)cm, and the small one has radius (C2 - 1)cm. By Pythagoras, in triangle OBE, OB C2, so OD = C2+ 1. OA = OD - AB = C2 + 1 - 2 = C2 - 1.