Problem Solving

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:17 am

Beth received 3/10 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?

A. 1/5
B. 2/7
C. 3/10
D. 7/20
E. 1/2

Answer: B
Source: official guide

Let's assign a "nice" value to the total number of votes cast.
We'll choose a number that works well with the given information.

Let's say that a total of 10 votes were cast.

Beth received 3/10 of the votes cast in a certain election
3/10 of 10 = 3.
So, Beth received 3 votes

What fraction of the OTHER votes cast would she have needed in order to have received 1/2 of the votes cast?
Receiving 1/2 of the votes would require Beth to get a total of 5 votes.
In other words, Beth would have needed 2 additional votes among the 7 people who didn't vote for her

Answer: 2/7 = B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:17 am

Beth received 3/10 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?

A. 1/5
B. 2/7
C. 3/10
D. 7/20
E. 1/2

Answer: B
Source: official guide

Solution:


We can let the total number of votes cast = 100. Thus, Beth received 30 votes, and she must receive 20 of the remaining 70 votes in order to have received 1/2 of the votes cast. Therefore, she must receive 20/70 = 2/7 of the remaining votes.

Alternate Solution:

Since Beth received 3/10 of the votes, there are 7/10 of the votes remaining, and we need to find the fraction of those 7/10 remaining votes she would have needed to have received ½ of all votes cast. Let’s let x = the fraction of those remaining votes that she needs. Thus, we have:

3/10 + (7/10)(x) = 1/2

Multiplying the entire equation by 10, we have:

3 + 7x = 5

7x = 2

x = 2/7

Answer: B