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# Amy and Jed are among 35 people, who are standing in a line, on behind

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Re: Amy and Jed are among 35 people, who are standing in a line, on behind [#permalink]
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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------|FRONT

Amy and Jed are among 35 people
We can write: x + y + z + Jed + Amy = 35 people
In other words, x + y + z + 2 = 35
Simplify: x + y + z = 33

The 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 Jed
x + y + Jed = 15
In other words: x + y + 1 = 15
Or: x + y = 14

Take:
x + y + z = 33
x + z = 24

Subtract the bottom equation from the top equation to get: y = 9

Take: x + y = 14
Since y = 9, we know that x = 5

Take: x + y + z = 33
Since y = 9 and x = 5, we know that z = 19

We have: BACK|-----5 people----JED------9 people------AMY----19 people people------|FRONT

How many people are in front of Jed?
The number of people in front of Jed = y + AMY + z
= 9 + AMY + 19
= 29

Cheers,
Brent
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Re: Amy and Jed are among the 35 people, who are standing in a line, one [#permalink]
Given

• There are 35 people including Amy and Jed
• Amy is in front of Jed, not necessarily in immediate front.

Let's say the line looks as follows

-------x people------- Amy ------- z people ------- Jed ------- y people-------

Question = z + x + 1 ?

Amy and Jed are among the 35 people

x + y + z + 2 = 35

x + y + z = 33 ---(1)

The number of people in front of Amy plus the number of people behind Jed is 24

x + y = 24 ---(2)

There are 15 people behind Amy, including Jed

z + 1 + y = 15

z + y = 14 ---(3)

(1) + (2)

x + y + z + y = 38

y = 38 - 35 = 5

x = 24 - 5 = 19

Therefore 19 + 5 + 1 = 29

IMO D
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Re: Amy and Jed are among 35 people, who are standing in a line, on behind [#permalink]
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Re: Amy and Jed are among 35 people, who are standing in a line, on behind [#permalink]
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