Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q15

At a party, only 4/9 of the invited guests came. The ratio of the number of women to the number of men present was 3 : 4. If 80 more men turned up for the party, the number of men would be twice the number of women. How many guests were invited?

Solution

Before 80 more men turned up

Women : Men

3 : 4

After 80 more men turned up

Women : Men

3 : 6

There was an increase of 2 units for men

2 units --> 80 (men)

1 unit --> 80 divided by 2 = 40

Total present at the party before 80 more men turned up

7 units --> 280

4/9 of invited guests --> 280

1/9 --> 280 divided by 4 = 70

All invited guests

9/9 --> 9 x 70 = 630

Answer: 630 guests

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