maths question...sorry

[Doowrah]

Please can someone explain this to me..The ratio of boys to girls at a party is 3:4. Six boys leave.Now the ratio is 5:8.How many girls were at the party?

[TodaysAGoodDay]

The ratio is 5:8. It was 6:8 (this is the same as 3:4)
So the ratio has dropped from 6:8 to 5:8

The number of boys (first number of ratio) that have left is 6, so the difference from 6:8 to 5:8 is 6. So each 1 = 6, so 1=6, 2=12, 3=18 and so on. Therefore the actual number is:

Ratio now: 5:8 which = 30:48

So therefore ratio at the beginning was 6:8 which means it was 36:48, so there were 36 boys and 48 girls.

Actually now I've read it back it looks quite complicated how I've explained it, but I hope you follow that.

[mineofuselessinformation]

First situation, the number of people is a multiple of seven. Second situation, the number of people is a multiple of thirteen. (Found by adding the numbers in the ratios).
You need to find a multiple of seven which when you take away five, give a multiple of thirteen as your starting point.
So 70 works for first situation, with 65 for second.
70 is 10 X 7, so originally there were 40 girls.

[mineofuselessinformation]

Oops, just realised I've worked it out for five leaving, not six! Poster above is correct. Sorry!

[partystress]

I am cross because I briefly knew the bar model method which makes this kind of Q really visual and simple, but can't remember it now! So instead, I looked for two numbers six apart which were multiples of 7 (cos 7 parts in a 3:4 ratio) and 13. The first pair I found were 84 and 78. So 84 split 3:4 is 36 boys, 48 girls. Take away six boys, 30 boys and still 48 girls.

[partystress]

Mineof clearly types faster than me!

[Doowrah]

2 different answers here can you see why I am confused.Thanks to both of you 'tho.

[Doowrah]

Ok no worries Mineof gawd bless you Todaysa.

[TodaysAGoodDay]

No, mineof, just no.

That means at the start there were 30 boys to 40 girls (3:4), and if 6 leave then it would be 24:40, or 48:80, which is not quite the same as 50:80

Sorry, but that's incorrect.

[TodaysAGoodDay]

Thatnks mineof, my maths is 'confused' sometimes too

[ToFindAndWakeTheDreamer]

Ok, so we have a party and play a game where the boys and girls have to form groups of the same number. Every group has to be the same and we want as few groups as possible. The boys form three groups and the girls form four groups. Each group has "x" number of children. 3:4 means 7 groups of "x" or 7x.

Now we take six of the boys away from one of the groups.

If a whole group of boys was now gone, there'd be a ratio of 2 groups of boys to 4 groups of girls. Playing by the rules, the two groups of boys could join together, and the girls would do the same. 1:2.

Only it isn't that simple, as we've been left with some boys left in the third group. So, we play the grouping game again to get the groups to all have the same number of children in them. This time we have to rearrange everyone into smaller groups. We now have 5 groups of boys and 8 of girls. 5:8. Each group has "y" children in it. We have 13 groups of "y". 13y.

So, what do we know so far?

7 groups of "x" minus 6 children is 13 groups of "y". This gives us our first equation.

7x - 6 = 13y

Now, the number of girls hasn't changed, so we know that:

4x = 8y

Or

x = 2y

We can put that into our first equation.

14y - 6 = 13y

Or

14y - 13y = 6

So

y = 6

We know there are 8y girls, so we do the last sum and get 8 * 6 = 48 girls!

[Doowrah]

So impressed by the maths competency on here and so sad that I find this so difficult.😓