Aarrrgh, maths block!

[mrtwisty]

Why can't I figure out this seemingly simple problem?:

In a class the ratio of boys to girls is 7:4
There are 9 more boys than girls.
How many children are there in the class?

How the hell do you work this out?

(Feel free to tell me I'm as thick as mince, I'm sure I deserve it on this occasion)

[Moonhawk]

Subtract 4 from 7 - gives you 3 difference.

Then divide the 9 overage by the 3 above - also gives you three.

Multiple both 7 and 4 by this second three - gives you:

21 boys and 12 girls - so there are 9 more boys in the class.

21+12 = 33 total

[grumbledoak]

7 - 4 = 3
=> 21 boys and 12 girls.

[Magic919]

If there were 7 boys and 4 girls, that would be 3 more boys. Go from there. Yes, you are thick.

[marshalla]

Total number of pupils = A

Number of boys, B = 7A/11

Number of girls, G = 4A/11

9 more boys than girls so B = G+9

So

A = B + G
A = G+9 + G = 2G+9

G+9=7(2G+9)/11
G+9=(14G+63)/11
11G+99=14G+63
(99-63)=(14G-11G)
36 = 3G
G=12
B=21

Edited by marshalla on Tuesday 2nd September 20:30

[mrtwisty]

Moonhawk said:

Subtract 4 from 7 - gives you 3 difference.

Then divide the 9 overage by the 3 above - also gives you three.

Multiple both 7 and 4 by this second three - gives you:

21 boys and 12 girls - so there are 9 more boys in the class.

21+12 = 33 total

Jesus Christ, why couldn't I see that!?!?!?

[Zwolf]

I thought of it in iterations of a sequence where the ratio remains constant:

1st iteration of 7:4. Difference is 3.
2nd iteration is 14:8. Difference is 6.
3rd iteration is 21:12. Difference is 9.

So the total in the class is the sum of 21 and 12. 33.

[mrtwisty]

Moonhawk said:

Subtract 4 from 7 - gives you 3 difference.

Then divide the 9 overage by the 3 above - also gives you three.

Multiple both 7 and 4 by this second three - gives you:

21 boys and 12 girls - so there are 9 more boys in the class.

21+12 = 33 total

Jesus Christ, why couldn't I see that!?!?!?

[Monkeythree]

A man employees two gardeners to cut his lawn. One is lazy and the other one is fast. Together it takes them 8 hours to cut the mans lawn. The man decides to sack the lazy gardener and asks the fast gardener to cut the lawn on his own. It takes him 12 hours.

How long would it have taken the lazy gardener to cut the lawn on his own?

[2 sMoKiN bArReLs]

Monkeythree said:

A man employees two gardeners to cut his lawn. One is lazy and the other one is fast. Together it takes them 8 hours to cut the mans lawn. The man decides to sack the lazy gardener and asks the fast gardener to cut the lawn on his own. It takes him 12 hours.

How long would it have taken the lazy gardener to cut the lawn on his own?

He wouldn't, because the fast one wouldn't be nagging him

[Zwolf]

Monkeythree said:

A man employees two gardeners to cut his lawn. One is lazy and the other one is fast. Together it takes them 8 hours to cut the mans lawn. The man decides to sack the lazy gardener and asks the fast gardener to cut the lawn on his own. It takes him 12 hours.

How long would it have taken the lazy gardener to cut the lawn on his own?

8F + 8L = 12F

Therefore 8L = 4F. In other terms L = 0.5F or F = 2L

Lazy gardener works at half the rate of the fast one, so it would take double the time the fast gardener took by himself: 24 hours.