SOLUTION: In a recent election between an incumbent and one opponent, the incumbent won by a ratio of 7 to 6. If the opponent won 30594 votes, how many votes did the incumbent win?

Question 243099: In a recent election between an incumbent and one opponent, the incumbent won by a
ratio of 7 to 6. If the opponent won 30594 votes, how many votes did the incumbent win?
Found 2 solutions by oberobic, MathTherapy:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
This can be set up using equal ratios:
7/6 = 30594/x
Cross multiply
7x = 30594*6
x = 30594*6/7 = 26223.43
Since you cannot have a partial vote, you can round to 26223.
...
Note that saying the ratio is 7/6 is very imprecise.
The concept of significant digits tells us that the number 7 to one significant digit means the value lies between 6.5 and 7.5. Likewise a value of 6 could be between 5.5 and 6.5. So a ratio of 7/6 could be as wide a range as 7.5/5.5. Clearly, 30594/26223 is within this range.
Answer by MathTherapy(10556) (Show Source): You can put this solution on YOUR website!
In a recent election between an incumbent and one opponent, the incumbent won by a
ratio of 7 to 6. If the opponent won 30594 votes, how many votes did the incumbent win?

Since the incubent won by a 7:6 ratio, then the incubent had 7 parts of the total votes, while the opponent had 6 parts of the total votes. Now, since the opponent's 6 parts is represented by 30,594 votes, using I as the incubent's votes, we can say that:

6I = 7 * 30,594 --------- Cross-mutiplying

I = 35,693

Therefore, I, or the incubent won votes.

---------
Check
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To check, you just need to realize that there are 13 (7 + 6) total parts, and that the incubent received of the 66,287 (30,594 + 35,693) votes that were cast between the two candidates, while the opponent received of the 66,287 votes that were cast between the two candidates.
_____________________________ OR ______________________________________

we can just simply set the ratio as the incubent's votes to the opponent's votes, which is 35,693:30,594, or 7:6, or , or .

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