Maths Olympiad Prep

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Algebra Difficulty 2.7 Junior Find the answer

There are 30 people in a room, 60\% of whom are men. If no men enter or leave the room, how many women must enter the room so that 40\% of the total number of people in the room are men?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since there are 30 people in a room and 60\% of them are men, then there are 610×30=18 \frac{6}{10} \times 30=18 men in the room and 12 women. Since no men enter or leave the room, then these 18 men represent 40\% of the final number in the room. Thus, 9 men represent 20\% of the the final number in the room, and so the final number of people is 5×9=45 5 \times 9=45 . Since 18 of these are men and 12 of these are the women originally in the room, then 451812=15 45-18-12=15 women entered the room.

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