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Schools Mathematics Grand Challenge

Week eight's Puzzles

There are 3 problems again this week. After last week's stinkers, we hope you'll find these a little easier! Next week we will be putting up the final set of puzzles.

Problem 16:

Three parties take part in a general election. Party A receives 40%, party B receives 30% and party C receives 30% of the votes cast in the election. Also:

(i) Of the people who voted for party A, 50% were women and 50% were men;
(ii) Of the people who voted for party B, 40% were women and 60% were men;
(iii) Of the people who voted for party C, 60% were women and 40% were men.

What percentage of the women who voted in the election voted for party B? Give your answer to the nearest percentage.

Problem 17:

There are 1,500 households in a housing estate. A certain number of the households have one car. Of the other households in the estate, 50% have two cars and the other 50% have no car. How many cars are in the housing estate in total?

Problem 18:

When you add up Jane's age, her mother's age and her father's age, their total age is 72. At the moment, Jane's father's age is 6 times Jane's age. When Jane's father's age is twice her age, the total age of the three of them will be twice what it is now. What is Jane's mother's age at the moment?


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