3rd June 2005 at 01:00
Oranges and lemons

Mrs Green made fruit squash for the village fete.

She spent pound;10 exactly on oranges costing 17p each and lemons costing 13p each.

She bought 20 more oranges than lemons.

How many oranges and lemons did Mrs Green buy in total?

Cherry ripe

Sally and Suzy shared an odd number of cherries.

They tossed a coin to decide who should have the extra cherry. Suzy said to Sally: "If I give you 4 of my cherries, you will have three times as many as I have left."

Sally said to Suzy: "If I give you 3 of my cherries, you will have twice as many as I have left."

One of the girls was lying and the other was telling the truth. Which girl was lying? If the girl who was telling the truth had the extra cherry, how many cherries did each girl have?

SOLUTIONS Oranges and lemons (ages 7 to 12) Mrs Green bought a total of 64 oranges and lemons. The possible ways of spending pound;10 on oranges at 17p and lemons at 13p are: 3 oranges + 73 lemons; 16 oranges + 56 lemons; 29 oranges + 39 lemons; 42 oranges + 22 lemons; and 55 oranges + 5 lemons.

To have 20 more oranges than lemons, she buys 42 oranges and 22 lemons.

Cherry ripe (ages 11 to 16) Suzy was lying. Sally had 8 cherries and Suzy had 7 cherries. Assume that the girls have x and x + 1 cherries. Suzy's statement indicates that 3(x - 3x + 4, or 3(x - 4x + 5, neither of which has an integral solution. Sally's statement indicates that 2(x - 3) = x + 4, or 2(x - 2x + 3, giving x = 10 or 7. Since Sally has the extra cherry, she has 8 cherries and Suzy has 7 cherries.

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