Please explain 600-700 level question-algebraic translation

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This question has stumped me. Does anyone have a good strategy for this?

On a team, the number of males is 3 fewer than twice the number of females. If one male were replaced by a female, there would be an equal number of males and females on the team. How many members are on the team?

a 14
b 12
c 10
d 9
e 7

Thanks!

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by deepakb » Tue Oct 05, 2010 10:42 am
The number of males is 3 fewer than twice the number of females.
M = 2F-3

If one male were replaced by a female, there would be an equal number of males and females on the team.
M-1 = F+1

Solve these two equation and you will get F= 5 and M= 7

How many members are on the team?
12

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by krazy800 » Tue Oct 05, 2010 10:45 am
rtaha2412 wrote:This question has stumped me. Does anyone have a good strategy for this?

On a team, the number of males is 3 fewer than twice the number of females. If one male were replaced by a female, there would be an equal number of males and females on the team. How many members are on the team?

a 14
b 12
c 10
d 9
e 7

Thanks!
IMO B

Male = M
Female = F

the number of males is 3 fewer than twice the number of females--- M=2F-3---(1)

If one male were replaced by a female, there would be an equal number of males and females on the team---M-1=F+1--(2)

Simplifying (2).. M=F+2

Substituting the value of M in (1) We get F=5.
Therefore M=7
M+F =12

HTH!!
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by Tani » Tue Oct 05, 2010 11:26 am
You could also backsolve this question quickly if you don't immediately see the formulas.
Tani Wolff