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### Number and algebra

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# Deep Roots

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### Rudolff's Problem

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Age 14 to 16

Challenge Level

Find integer solutions to: $${{\sqrt{a + b\sqrt{x}}} + {\sqrt{c + d\sqrt{x}}}} ={ 1}$$

Hint: As everything on the left is positive and the total is 1, there are only a few cases to consider.

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?