Please explain 600-700 level question-algebraic translation

[rtaha2412]

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!

[deepakb]

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

[krazy800]

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!!

[Tani]

You could also backsolve this question quickly if you don't immediately see the formulas.