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

Answer Verified Verified
Hint: Ratio means the relation between two or more numbers which shows that which number is greater and by how much .
Here 5 to 3 means 5:3 or it can be written as $\dfrac{5}{3}$

Complete step-by-step solution
Total number of votes = 120,000
Let the common ratio be ‘x’
As Gracia won the election against Prez by a ratio of 5 to 3
Then ,
Number of votes cast for Gracia = $5\times x$ = 5x
Number of votes cast for Prez = $3\times x$ = 3x
To find the number of votes first we have to find the value of x
Total number of votes cast = number of votes cast for Garcia + number of votes cast for Prez
= 5x + 3x
= 8x
Since total number of votes cast is 120,000
Therefore ,
120,000 = 8x
X = $\dfrac{120,000}{8}$
X = 15,000
Now , number of votes cast for Prez = 3x
= $3\times 15,000$
= 45,000
Therefore , the number of votes cast for Prez is 45,000

Hence , the correct answer is option ( C )

Note: In such type of question assume common ratio and apply the relation :
Total quantity = sum of each quantity
And here in this problem we can write as :
Total number of votes cast = number of votes cast for Garcia + number of votes cast for Prez.