Bunuel wrote:
Amy and Jed are among 35 people, who are standing in a line, on behind the other, waiting to buy movie tickets. The number of people in front of Amy plus the number of people behind Jed is 24. If there are 15 people behind Amy, including Jed, how many people are in front of Jed?
A. 23
B. 25
C. 27
D. 29
E. 31
We are told that Jed is standing behind Amy.
Let x = number of people behind Jed
Let y = number of people ahead of Jed but behind Amy
Let z = number of people ahead of Amy
So, our diagram looks like this:
BACK|-----x people----JED------y people------AMY----z people------
|FRONTAmy and Jed are among 35 peopleWe can write: x + y + z + Jed + Amy = 35 people
In other words, x + y + z + 2 = 35
Simplify:
x + y + z = 33The number of people in front of Amy plus the number of people behind Jed is 24.We can write:
x + z = 24 There are 15 people behind Amy, including Jedx + y + Jed = 15
In other words: x + y + 1 = 15
Or:
x + y = 14Take:
x + y + z = 33 x + z = 24 Subtract the bottom equation from the top equation to get:
y = 9Take:
x + y = 14Since
y = 9, we know that
x = 5Take:
x + y + z = 33Since
y = 9 and
x = 5, we know that
z = 19We have:
BACK|-----
5 people----JED------
9 people------AMY----
19 people people------
|FRONTHow many people are in front of Jed? The number of people in front of Jed =
y + AMY +
z =
9 + AMY +
19= 29
Answer: D
Cheers,
Brent