Question

Anna, Ivan and Elena are running for class president. On Thursday night Anna had 20% of the votes, Ivan had 35% of the votes and Elena had 45% of the votes. On Friday, final votes were added to the counts and all of them favored Elena. If in the end Anna had 16% of all votes, what percent of the voters chose Ivan?

Answer 1

28%

Explanation:

On Thursday night Anna had 20% of the votes, Ivan had 35% of the votes and Elena had 45% of the votes. You can take the number of total votes on Thursday equal to 100, then Anna had 20 votes, Ivan had 35 votes and Elena had 45 votes.

Let x be the number of votes added on Friday. All of them favored Elena, then Elena in total had 45+x votes and the number of all votes became 100+x. In the end Anna had 16%, then

100+x - 100%,

20 - 16%.

Write a proportion:

`(100+x)/(20)=(100)/(16),\\ \\16(100+x)=2000,\\ \\1600+16x=2000,\\ \\16x=400,\\ \\x=25.`

Find the percent of the voters that chose Ivan:

125 - 100%,

35 - y%.

Write a proportion:

`(125)/(35)=(100)/(y),\\ \\125y=35\cdot 100,\\ \\y=(35\cdot 100)/(125)=(35\cdot 4)/(5)=7\cdot 4=28\%.`