Another word problem - application of linear equations

[paulmdrdo1]

The annual sophomore class picnic is planned by a committee consisting of 17 members. A vote to determine whether the picnic should be held at the beach location or in the mountains resulted in a victory for the beach location. However, if two committee members had changed their vote from favoring the beach to favoring the mountains, the mountain site would have won by vote. How many votes did each picnic location receive?

1st solution

let $x =$ vote for beach location
$17-x =$ vote for mountain location

if two committee members had changed their vote from favoring the beach to favoring the mountains, the mountain site would have won by vote.

$x-2= $new vote for beach location
$(17-x)+2= $new vote for mountain location

$19-x=(x-2)+1$

$x=10$ votes for beach

$7 $ votes for mountain

2nd solution

$(17-x)+1=x-2$

$x=10$ votes for beach

$7 $ votes for mountain

which solution method is correct?

 

[MarkFL]

Thread titles like "Word problem" or "Another word problem" don't really describe the type of problem being posted. Please take a moment to choose titles the describe the problems being posted. You are more likely to get prompt help if your title let's those reading the forums know a bit about the nature of the problem.

I would let $B$ be the number who voted for the beach location and $M$ be the number who voted for the mountain location.

We know:

$B+M=17$

$B-2=M+2-1$

You will get the same result as your method(s) which are equivalent to the above. :D

 

[HallsofIvy]

Both of your methods are perfectly valid. They are just different ways of looking at the same data.

(So its a good thing they give the same answer!)