Question

A total of $120,000$ votes were cast for $2$ opposing candidates, Garcia and Prez. If Garcia won by a ratio of $5$ to $3$, what was the number of votes cast for Prez?

• A. 15,000
• B. 30,000
• C. 45,000
• D. 75,000
• E. 80,000

Answer 1

The correct option is C 45,000

Let the common ratio be ${}^{\prime }{x}^{\prime }$

As Garcia won against Prez by a ratio of $5$ to $3$,

Number of votes cast for Garcia $=$ $5x$

Number of votes cast for Prez $=$ $3x$

To find ${}^{\prime }{x}^{\prime }$,

Total number of votes cast $=$ Number of votes cast for Garcia $+$ Number of votes cast for Prez

$=$ $5x$ $+$ $3x$

$=$ $8x$
But, Given that

Total number of votes cast $=$ $120,000$

From above,

$8x$ $=$ $120,000$

$8$ $\times$ $x$ $=$ $120,000$

$x$ $=$ $\frac{120,000}{8}$

$x$ $=$ $15,000$

Now, number of votes cast for Prez $=$ $3x$

$=$ $3$ $\times$ $x$

$=$ $3$ $\times$ $15,000$

$=$ $45,000$

Therefore, the number of votes cast for Prez was ${}^{\prime }45,{000}^{\prime }$.