1. ## I tried doing this 3 times already!!!

In a recent election, Abby received 46 more votes than Barbara. If a total of 480 votes were cast for the two candidates, find out how many votes each candidate received.

a) Write the equation you would use to solve this problem, using ${b}$ as the number of Barbara's electoral votes. __________

b) After solving the equation, how many votes did Barbara receive? ________

c) After solving the equation, how many votes did Abby receive? __________

2. ## Re: I tried doing this 3 times already!!!

What 2 equations did you initially write down from the given information?

3. ## Re: I tried doing this 3 times already!!!

Originally Posted by MarkFL2
What 2 equations did you initially write down from the given information?

B+46-b=480

4. ## Re: I tried doing this 3 times already!!!

Let $\displaystyle a$ be the number of votes for Abby, and $\displaystyle b$ be the number of votes for Barbara.

We are told "Abby received 46 more votes than Barbara" which gives us:

$\displaystyle a=b+46$

We are told "a total of 480 votes were cast for the two candidates" which gives us:

$\displaystyle a+b=480$

Substituting for $\displaystyle a$ from the first equation into the second gives us:

$\displaystyle b+46+b=480$

Now, you may solve for $\displaystyle b$...

5. ## Re: I tried doing this 3 times already!!!

Originally Posted by MarkFL2
Let $\displaystyle a$ be the number of votes for Abby, and $\displaystyle b$ be the number of votes for Barbara.

We are told "Abby received 46 more votes than Barbara" which gives us:

$\displaystyle a=b+46$

We are told "a total of 480 votes were cast for the two candidates" which gives us:

$\displaystyle a+b=480$

Substituting for $\displaystyle a$ from the first equation into the second gives us:

$\displaystyle b+46+b=480$

Now, you may solve for $\displaystyle b$...

b+46+b=480
-46 -46

b+b=434
2b/2 434/2

B=217

6. ## Re: I tried doing this 3 times already!!!

Correct, now you can use the original first equation to find a...