Question

There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys is 5:3.There are 178 more Chinese boys than Malay boys.How many girls are there in the hall?

Answer 1

first step: express the clues algebraically:

boys/girls = 2/3
cboys/mboys = 5/3
cboys = mboys+178

Now, we want to find the number of girls. Just for ease of algebra, let's change the above to

b/g = 2/3
c/m = 5/3
c = m+178

3c = 5m
3(m+178) = 5m
2m = 534
m = 267

So, there are 267 Malay boys and 445 Chinese boys. That means b=712.

Now, we know that 3b=2g, so

g = 3/2 * 712 = 1068

So, there are 1068 girls in the hall.