KJSEA 2025 Maths Q23 — Ratio of Men to Women to Children

KJSEA 2025 Grade 9 Numbers

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The Question

“At a Thanksgiving ceremony, the ratio of men to women to children was 5:7:3. There were 60 children present. Find (a) the number of men, (b) the number of women, and (c) how many more women than men attended the ceremony.”

1

Find the value of one part

The ratio 5:7:3 divides everyone into equal-sized parts. Children are given as 3 parts and we know that these 3 parts stand for 60 children. So to find how many people make up a single part, we divide the number of children by their number of parts.

3 parts=60⇒1 part=603=203 \text{ parts} = 60 \Rightarrow 1 \text{ part} = \frac{60}{3} = 20

Every part in this ratio is worth the same number of people, so once you know one part you can find any group.

2

Work out the number of men

Men correspond to 5 parts of the ratio. Since each part is 20 people, multiply the number of parts for men by the value of one part.

Men=5×20=100\text{Men} = 5 \times 20 = 100
3

Work out the number of women

Women correspond to 7 parts of the ratio. Multiply their number of parts by the value of one part in the same way.

Women=7×20=140\text{Women} = 7 \times 20 = 140
4

Compare women and men

The last part asks how many more women than men there were. Subtract the number of men from the number of women to get the difference.

Difference=140−100=40\text{Difference} = 140 - 100 = 40

Final Result

There were 100 men and 140 women, which means there were 40 more women than men at the ceremony.

Why this method works

A ratio only tells you how a total is split into equal shares, not the actual numbers. The trick is to find the value of a single share, and the easiest place to start is the group whose count you already know — here the children, whose 3 shares equal 60, so one share is 20 people. Because every share in a ratio is equal, that same value of 20 unlocks every other group: multiply it by each group's number of parts. This is why sharing-in-a-ratio problems always reduce to the same two moves — find one part, then scale it up.

✓

Add the groups: 100 men + 140 women + 60 children = 300 people, and 300 divided into 5+7+3 = 15 parts gives 20 per part, matching our value of one part.