Question

In a recent election, Ms. Robbins received $8,000$ votes cast by independent voters, that is, voters not registered with a specific political party. She also received $10$ percent of the votes cast by those voters registered with a political party. If $N$ is the total number of votes cast in the election and $40$ percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?

• A. $0.06N+3,200$
• B. $0.1N+7,200$
• C. $0.4N+7,200$
• D. $0.1N+8,000$
• E. $0.06N+8,000$

Answer 1

The correct option is E $0.06N+8,000$

$\Rightarrow$ Ms. Robbins received $8,000$ votes from independent voters.

$\Rightarrow$ $40\%$ of $N$ are independent voters.

$\therefore$ $60\%$ of $N$ are not independent voters. From this group Ms. Robbins received $10\%$ votes.

$\Rightarrow$ So, Total votes = $(\frac{10}{100}\times \frac{60}{100})N+8000$

$\Rightarrow$ $Totalvotes=(0.1\times 0.6)N+8000$

$\therefore$ $Totalvotes=0.06N+8000.$