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What's My Weight?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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Oranges and Lemons

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Grandpa's Rock Cakes

Stage: 2 and 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
The cake weighed 5 130g.

The range of the guesses (5 040g, 5 060g, 5 110g, 5 120g and 5 150g) is just 100 so the two 'wild' estimates must both be low or both high.

Since the difference between 5 040 and 5 060 is 20, 5 040 is 90 out and 5 060 is 70 out.

This problem is taken from the UKMT Mathematical Challenges.