In a recent election corrine brown received 13,707 more votes than bill Randall . If the total number of votes was 119,537 , find the number of votes for each candidate

Answer 1

Hi...

Your problem here requires solving TWO SIMULTANEOUS equations; I will use the initials of the candidates for the variables but you can use X and Y, just be sure to remember which belongs to whom. The simplest way is to use the SUBSTITUTION METHOD.

1. CB = Votes that Corrine Brown received
2. BR = Votes that Bill Randall received

We know that the TOTAL number of VOTES = 119,537, that is CB + BR =119,537 (Eq 1)

We know that CB received 13,707 more votes than BR, that is CB = BR + 13,707 (Eq 2)

Since ONE equation is already in terms of the OTHER variable (Eq 2), plug that into (Eq 1) and solve for the FIRST variable (BR). Then use the value of BR into the SECOND equation to find the value of the SECOND variable (CB.) and ALWAYS check your math!

1. CB + BR =119,537
2. (BR + 13,707) + BR = 119,537
3. 2BR + 13,707 = 119,537
4. 2BR = 119,537 - 13,707
5. 2BR = 105,830 ....so BR = 105,830/2 = 52,915 - This is how many votes Bill Randall rec'd

In turn, CB = = BR + 13,707 = 52,915 + 13,707 = 66,622 - This is how many votes Corrine Brown rec'd

CHECK

CB + BR =119,537

66,622 + 52,915 = 119,537

Hope this helps... :)

Answer 2

Let:

C= Amount of Votes for Corrine Brown

B= Amount of Votes for Bill Randall

Since we have 2 unknowns, we must have 2 equations relating them in order to solve.

{Eq. 1}......C + B = 119,537 votes (The total number of votes is equal to the sum of the votes for each candidate)

{Eq. 2}.......C = B + 13,707 votes (Corrine Brown received 13,707 more votes than Bill Randall)

Plugging in Equation 2 into Equation 1:

(B + 13,707) + B = 119,537

Solving for B:

2*B + 13,707 = 119,537

Subtract 13,707 from both sides:

2*B = 105,830

Divide by 2 to isolate B:

B = 52,915 votes

Plugging this value of B into Equation 2:

C = (52,915) + 13,707

C= 66,622 votes

Conclusion:

Corrine Brown received 66,622 votes

Bill Randall received 52,915 votes

Answer 3

To do this problem, we can set up a basic equation:

Since the total votes is 119,537 and Corrine Brown Received 13,707 votes more, our equation can read:

119,537=x+(x+13,707)

119,537=2x+13,707

-13,707 -13,707

105,830=2x

52,915=x

Now that we found x, we can use this to find the amount of votes. Since Corrine Brown received 13,707 MORE votes we can add it to our x.

13,707+52,915=66,622

So, Corrine Brown received 66,622 votes and Bill Randall received 52,915 votes.