Remember your Prom?

[dtweah]

An equal number of boys and girls attended the senior prom. If 40% of the seniors who attended were girls and 30% of the non-seniors who attended were boys, what fraction of the girls were seniors?

(a) 2/5
(b) 7/10
(c) 5/11
(d) 8/15
(e) 3/8

[Vemuri]

IMO D.

Lets assume there are 100 students & X of them are Seniors and the rest (100-X) are Juniors.

0.4X --> Senior girls, i.e. 0.6X are Senior boys.
0.3(100-X) --> Junior boys, i.e. 0.7(100-X) are Junior girls.

The question stem tells us that the # of boys are girls is equal.
==> 0.4X+0.7(100-X) = 0.6X+0.3(100-X)
==> X=200/3

We are asked to find what fraction of girls are seniors, i.e. (Senior girls) /(Total # of girls)
==> 0.4X/(0.4X+0.7(100-X))
Substitute the value of X & you will get the answer as [spoiler]8/15[/spoiler]

[m&m]

agreed with D

2 eqns - let x be seniors and y be non-seniors
0.6x+0.3y = 50%
0.4x+0.7y = 50%

x/y = 2/1

so 66%=2/3 of attendees are seniors
2/3*4/10 = 4/15 of the ENTIRE population

so of just girls it's 4/15*2 = 8/15

it makes much more sense when you draw it in a 3x3 matrix

[dtweah]

An equal number of boys and girls attended the senior prom. If 40% of the seniors who attended were girls and 30% of the non-seniors who attended were boys, what fraction of the girls were seniors?

(a) 2/5
(b) 7/10
(c) 5/11
(d) 8/15
(e) 3/8

B=G so Total number attendees =2G. Let NS= Non Seniors

S + NS= 2G ----1

40%S = SG--- S=5SG/2

70%NS= NSG-- NS =10NSG/2. Into 1 gives

5SG/2 + 10NSG/2= 2G
SG + NSG = G

35 SG + 20NSG =28G
-20SG -20 NSG =-20G

15 SG =8G

SG=8G/15

Choose D.

[dumb.doofus]

Just another approach using table

------------- Boys-----girls---total
Seniors-------0.6y-----0.4y-----y
Non-seniors---0.3z-----0.7z-----z
Total---------x--------x

0.6y + 0.3z = 0.4y + 0.7z => y = 2z --- (1)

Ratio = 0.4y/(0.4y+0.7z).. substituting equation (1) and solving gives

Ratio = 8/15