# How many participated in the referendum?

#### Sara33

##### New member
In a referendum the no alternative got 1 000 000 more votes than the yes alternative. If 50 000 of the yes voters had voted no , then the no alternative would have gotten twice as many votes as the yes alternative. How many participated in the referendum?

This is my attempt:
yes=x
no=y

y=x + 1 000 000
2 y = x + 1 050 000

This is however incorrect. Where is my error? I know how to solve simultanious equations and I only need help with writing the first to equations. Thank you in advance!

#### tkhunny

##### Moderator
Staff member
2(y+50000) = (x - 50000)

You can't just invent voters. If they move, they must have moved from somewhere.

#### Sara33

##### New member
tkhunny said:
2(y+50000) = (x - 50000)
The 2 should be on the other side. Thank you for your help! Soroban has also send me an email and explained how to do it.

#### tkhunny

##### Moderator
Staff member
Excellent. I didn't complete the solution after I wrote that. Had I, surely I would have noticed that negative 1,000,000 voters was a bad idea. Is that how you found the error?

I already spent some time in the corner, so no one suggest it.

#### Sara33

##### New member
Soroban send me an email and explained how to solve it. I compared the different equations you two had written and I thought the 2 should be on the right hand side. However I did the same mistake as you in the beginning.

#### tkhunny

##### Moderator
Staff member
So, what you are saying is:

1) You actually could have done it yourself, otherwise you couldn't have known that my original equation was wrong.

2) You still waited for someone else to show you how to do it, even though you knew already, rather than figuring it out for yourself.

3) Soroban is acting subversively to undermine the efforts of other volunteers, rather than his usual M.O. of just providing complete public solutions that require nothing from the student.

#### Sara33

##### New member
1) No I did not understand the question from the beginning, however when soroban wrote the equation with the 2 on the other side, I tried to solve the equation and the answer were correct.
2) No I did not know it. When I logged in I had an answer from you and from soroban and I read both of them.

My only aim is to learn and understand as much mathematics as possible. The original math question was not a homework, I went to the libary and borrowed a few books so I can prepare for my exam.

#### Denis

##### Senior Member
Sara, may I "arm you" with this tip :

often much easier if you "make up" a simpler but similar problem to the one you're given; like:
y = yes voters
n = no voters

n = 270
y = 150
OK: n = y + 120 [1]
SO: In a referendum the no alternative got 120 more votes than the yes alternative.

Now "move enough" to leave n = 2y:
n + 10 = 280
y - 10 = 140
OK: n + 10 = 2(y - 10) [2]
SO: If 10 of the yes voters had voted no , then the no alternative would have gotten twice as many votes as the yes alternative. How many participated in the referendum?

To solve, substitute [1] in [2]: y + 120 + 10 = 2y - 20 ; y = 150 ; so n = 150 + 120 = 270 ; total = n + y

Now go back to original problem: it'll be just as easy; get my drift?

#### Sara33

##### New member
Thank you Denis, that was a good advice!