MHB Election Outcome Hinges on Vote Ratios: Can You Solve It?

[Ilikebugs]

In a recent election, the ratio of the number of voters for the Purple Party to the
number of voters for the Pink Party was 15:16 and the Pink Party won the
election. Had 300 more people voted for the Purple Party and 200 fewer people
voted for the Pink Party, the ratio would have been 11:10 and the Purple Party
would have won the election.
Determine the total number of votes originally cast.If A=purple and B=pink, I got A*(15/16)=B and (A+300)*(10/11)=B-200, but when I went through I didn't get the right answer.

 

[Jameson]

In a recent election, the ratio of the number of voters for the Purple Party to the
number of voters for the Pink Party was 15:16 and the Pink Party won the
election. Had 300 more people voted for the Purple Party and 200 fewer people
voted for the Pink Party, the ratio would have been 11:10 and the Purple Party
would have won the election.
Determine the total number of votes originally cast.If A=purple and B=pink, I got A*(15/16)=B and (A+300)*(10/11)=B-200, but when I went through I didn't get the right answer.

Hi there. :)

Look at the part in red to start with. This kind of issue comes up a lot with word problems.

We know that the ratio of purple party to pink party is 15:16, which means that the purple party has less people. So in order to make the two parties equal we need to multiply the purple party by something greater than 1, not smaller. In other words, we need to scale up the purple party to match the pink party. So I think the first equation would be:

$$A = \frac{15}{16}B$$

What do you think? Do you see any other places you could tweak?

 

[Ilikebugs]

(10/11)a+(5200/11)=b

?