SOLUTION: 70% of girls want to go to prom and 40% of boys want to go to prom. Is it possible that only 50% of the students wanted to go to prom?

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Question 378521: 70% of girls want to go to prom and 40% of boys want to go to prom. Is it possible that only 50% of the students wanted to go to prom?
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
yes

.7g + .4b = .5(g + b)

.7g + .4b = .5g + .5b

.2g = .1b

2 = b/g

the percentages work if the boy/girl ratio is 2/1

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
70% of girls want to go to prom and 40% of boys want to go to prom.
Is it possible that only 50% of the students wanted to go to prom?
:
I think so:
:
Try a test case, say there are 240 students
let x = no. of girls
then
(240-x) = no. boys
.7x + .4(240-x) = .5(240)
.7x + 96 - .4x = 120
.3x = 120 - 96
.3x = 24
x =
x = 80 girls,
then
240-80 = 160 boys
:
:
See if that works
.7(80) + .4(160) = .5(240)
56 + 64 = 120, which is 50% of the student body