Maths problem

KuenMa

Can anyone help with the following problem?

At a party, the ratio fo the number of boys to the number of girls was 3:4.   When another 5 boys and 5 girls joined the party, the ratio becamde 7:9.  How many boys were there at the party at first?

Thanks.

Kuen Ma

StrongCat

Do not know any smart way to do it. My try:
4X = 3Y   ---- equation 1
9(x+5) = 7(y+5)  ---- equation 2
substitues x in equation 2 by equation 1
The answer: Y=girl=40.

KuenMa

StrongCat,

Thanks for your suggestion.   I tried this method as well.  However,
the teacher said there are some easier ways to solve the problem.
So I just post it out to ask for help.

Thanks again for your help.

Kuen Ma

lillymarie

try do it this way

7:9
=14:18
=21:27
=28:36
=35:45

Both sides minus 5 will have ratio of 3:4
So number of boys is 30 and number of girls is 40.

LingChiBaBa

Let x = no.of boys at first,

Total number of boys and girls at first = 7x/3
Total number of boys and girls after join = 16(x+5)/7

7x/3 + 10 = 16(x+5)/7
x/21 = 10/7
x = 30

StrongCat

Keen Ma,

If u got the 'simple' method, pls share with us. Could u ask your kid to check it out with classmate/ teacher afterward? Which level of Math question is it?

Thanks

KuenMa

Thanks all for your reply.    I have asked my son to check with the teacher.
The teacher showed him some workings on his exercise book but he still could not get it.    When my son asked again, the teacher seemed to be annoyed and asked him to think again.     

The only thing to do maybe to wait for the return of the exercise book and check what the teacher had written down.     I wonder would it be some Olympic Maths method.      Will share with you when the book is returned.
By the way, it is a P6 maths problem.

Kuen Ma