In November 1994, the first live concert on the Interent by a major rock n roll band was broadcast. Most fans stand in lines for hours to get tickets for concerts. Suppose you are in line for tickets. There are 200 more people ahead of you than behind you in line. the whole line is three times the nubmer of people behind you. how many people are in line for concert tickets?

Question

Can you please explain the easiest ways to solve these types of problems, step by step. I have a test tommorow, and I would really like to learn this.

Please and thank you. :)

Answer 1

Look for ways to express given values.
If there are two things you are trying to find out, try to express one of them in terms of the other. Solve the equation of one variable, then use the relationship to find the other variable.

Let x = number in back of you.
Let y = number in front of you.

It is given that the number of people in front of you are 200 more than the people in back of you.

y = x + 200

the whole line is 3 * x

The total line can be expressed two ways
x + y
and
3 * y

so x + y = 3 * x
or
y = 2x

going back to y = x + 200
express y in terms of x
2x = x + 200
x = 200
y = 400
the line is x = y = 600

Answer 2

Here is a drawing. The | marks where you stand. Let x = number behind, then x + 200 = number in front.
--------|-----------

The total number is x + x + 200.

the problem states that the total number is the same as 3 times the those behind. So 3x = x+x+200
solve for x. I get 200.
So 200 must be behind. 200+x or 400 must be in front. The total must be 200 + 400 = 600. And you can check by 3 times the number behind is the total and 3x200 = 600