2.8 voters

[lisahayes]

In an election, 2.8 million votes were cast and each vote was for either Candidate 1 or Candidate 2. Candidate 1 received 28,000 more votes than Candidate 2. What percent of the 2.8 million votes were cast for Candidate 1.

I was thinking to solve it this way ...

x + x + 28,000 = 2,800,000
2x + 28,000 = 2,800,000
2x= 28,000-2,800,000
2x= 2,772,000
x=1,386,000

Candidate 1 = 1,386,000+28,000=1,414,000

1,414,000/2,800,000 =50.5 percent

 

[BigGlenntheHeavy]

\(\displaystyle Let \ x \ = \ candidate \ 1 \ and \ y \ = \ candidate \ 2.\)

\(\displaystyle Then \ x \ + \ y \ = \ 2.8E6 \ and \ x \ = \ y+28E3\)

\(\displaystyle Solving \ the \ above \ system \ gives \ x \ = \ 1,414,000 \ and \ y \ = \ 1,386,000\)

\(\displaystyle Check: \ 1,414,000+1,386,000 \ = \ 2,800,000 \ and \ 1,414,000-1,386,000 \ = \ 28,000.\)

\(\displaystyle Hence, \ \frac{1,414,000}{2,800,000} \ = \ ,505 \ = \ 50.5\% \ of \ the \ vote \ went \ to \ candidate \ 1..\)