Ratios

Q: In a seminar, the ratio of the number of men to the number of women was 2:3. On the following day, two more men attended the seminar. The ratio became 5:6. How many participants were there in the seminar at first?

Understanding the question

This is a question about ratio. The ratio has changed because the number of men has changed. Thus, steps to solve this question are:

1. Make the ratio with the same number of women on the first and second day of the seminar. It is because the number of women is unchanged.

2. Find out the change (difference) of the number of men on the first and second day of the seminar.

3. The difference of the number of men on the first and second day is 2, which is also equivalent to the answer from step 2.

4. Find the number of participants on the first day.

Step-by-step Answer

1. The men-women ratio on the first day => 2:3 = 4:6

The men-women ratio on the second day => 5:6

2. Comparing the men-women ratio on the first and second day => 4:6 and 5:6

The difference of the number of men on the first and second day = 5 - 4 = 1

3. 1 unit of difference = 2 more men attended the seminar on the second day.

4. Total units on the first day = 4 + 6 = 10

Total participants on the first day = 10 x 2

= 20 participants

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Checking the answer

On the first day, there were 20 participants with the ratio 2:3. Thus, the number of men on the first day was (20 x 2) � 5 = 8.

On the second day, two more men attended the seminar. Thus, the number of men on the second day was 2 + 8 = 10.

The number of women on the first and second day was = 20 - 8 = 12.

The men-women ratio on the second day = 10:12

= 5:6

Thus, the answer, 20 participants, is correct.

Note to parents: If your child encounters difficult questions, asks him / her to check the answer. Checking the answer is a good way to reassure your child that he / she has answered the question correctly