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Algebra Difficulty 2.5 Junior Find the answer Canada

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?

Pick one

Solution

Since there are 30 people in a room and 60% of them are men, then there are $\frac{6}{10}\times 30 = 18$ 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 $5\times 9 = 45$ .

Since 18 of these are men and 12 of these are the women originally in the room, then $45 - 18 - 12 = 15$ women entered the room.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.