Fair shares

1 Carole and Rupee are going to London on the train. They decide to share the cost of a taxi to the station and back. Carole lives exactly half way between Rupee’s house and the station. Rupee gets in first and pays the driver Pounds 12 for the return journey. What should Carole pay Rupee as her fair share of the cost?

2 A group of friends share equally the cost of a pound;24 meal. If the number of friends in the group were doubled, each student would pay pound;2 less. How many friends are there in the group?

Weigh in

Before the races, four jockeys stood on the scales.

Nick and Tim together weighed the same as Andrew and Simon. Nick and Andrew together weigh more than Tim and Simon. Andrew weighs less than Simon.

Who was the heavier? Arrange the four jockeys in order.

SOLUTIONS Fair shares (Ages 8 to 12). 1 pound;4. For half of the return journey, Rupee is solely responsible for the fare. For the other half, Carole and Rupee are jointly responsible. So Carole should pay pound;4 and Rupee should pay pound;8. 2 There are 6 friends in the group. Twice as many friends would each pay half as much. If pound;2 is half the cost of a share, pound;4 is the full cost. So there must be 6 friends in the group to pay pound;24 between them.

Weigh in (Ages 13 to 16). Nick is the heaviest, then Simon, then Andrew, then Tim. Given that N+T=A+S (1), or S+A=N+T (2). We are also given then N+A

T+S (3) and S

A (4). Subtracting (1) from (3) gives A

T (5).

Subtracting (2) from (3) gives N

S (6). Combining (4), (5) and (6) gives N

S

A

T.