Peru and Egypt took part in Youth Games. From Peru, the ratio of the number of male supporters to the number of female supporters was 4 : 1. From Egypt, the ratio of the number of male supporters to the number of female supporters was 1 : 7. The total number of supporters from Peru was ⁵₂₄ the total number of supporters from Egypt.

1. What was the ratio of the number of male supporters from Peru to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 294 male supporters from both countries joined the games, the percentage of all the female supporters became 44%. How many less female supporters from Peru than Egypt were there at first?

Peru		Egypt
5 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
4	1	1x3	7x3
4 u	1 u	3 u	21 u

(a)
Number of male supporters from Egypt
= ¹₈ x 24 u
= 3 u

Number of female supporters from Peru
= ⁷₈ x 24 u
= 21 u

Total number of male supporters
= 4 u + 3 u
= 7 u

Male supporters from Peru : Total male supporters
4 : 7

(b)

	Male supporters	Female supporters
Before	7x2 = 14%	22x2 = 44%
Change	+ 294
After	56%	44%

Number of male supporters in the end in percent
= 100% - 44%
= 56%

Total number of female supporters at first
= 1 u + 21 u
= 22 u

After another 294 male supporters from both countries joined the games, the percentage of all the female supporters became 44%.

Since only more male supporters joined the games, the number of female supporters remains unchanged. Make the number of female supporters the same.

22 u = 44%

1 u = 44% ÷ 22 = 2%

Number of male supporters at first in percent
= 7 x 2%
= 14%

Number of male supporters from both countries who joined the games
= 56% - 14%
= 42%

42% = 294 

1% = 294 ÷ 42 = 7

Number of less female supporters from Peru than Egypt at first
= 21 u - 1 u
= 20 u
= 20 x 2%
= 40%
= 40 x 7
= 280 

Answer(s): (a) 4 : 7; (b) 280