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Here 5 to 3 means 5:3 or it can be written as $\dfrac{5}{3}$

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

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.