fractions

finance wrote:If Kelly received 1/3 more votes than Mike in a student election, which of
the following could have been the total number of votes cast for the two
candidates?

(A) 12 (B) 13 (C) 14 (0) 15 (E) 16

The answer choices are small, so we can guess and check.

Let K=Kelly and M=Mike.
Since K received 1/3 more votes than Mike, M must be a multiple of 3.
Let M = 6.
Since (1/3)*6 = 2, K = 6+2=8.
M+K = 6+8 = 14.

The correct answer is C.

Answer is [spoiler](C)[/spoiler]

Kelly received 1/3 more votes than Mike. Let K be the # of kelly's votes and M be the # of mike's votes
K=M+M/3
K=4M/3 and M=3K/4

Total # of votes cast is M+K= X....(1)
Substituting K=4M/3 in this equation we get
7K/4=X
or
K=4X/7....(a)

Substituting M=3K/4 in equation (1) we get
7M/3=X
or
M=3X/7....(b)

Now the total number of votes recvd by mike and kelly individually are definitely integers. So we substitute each of the answer choices as the value of X in (a) and (b) and the one that gives both M and K as integers is the correct answer. In this case 14 returns an integer value for both K and M. Hence C

k = m + 1/3 m = 4/3m

thus 4/3 m + m = T

hence m = 3/7 * Total

hence 14 fits the bill.

Kelly = 1+1/3 =4/3

Mike = 1


K:M

4/3 : 1 (x 3)

4:3 total of ratio 7

so answer must be a multiple of 7

only 14 works