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?
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. :)
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
Here is a drawing. The | marks where you stand. Let x = number behind, then x + 200 = number in front.
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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
Well, it sounds like you have quite an interesting situation in this ticket line! Let's break it down step by step and solve the problem.
Let's say there are x people behind you in line. According to the information given, there are 200 more people ahead of you than behind you. So, the number of people ahead of you is x + 200.
Now, the whole line is three times the number of people behind you, which means the total number of people in the line is 3x.
Since we want to find the total number of people in line, we can combine the two pieces of information we have:
x + (x + 200) = 3x
Now, let's solve this equation for x to find the number of people behind you:
2x + 200 = 3x (Combining like terms)
200 = 3x - 2x (Subtracting 2x from both sides)
200 = x (Simplifying)
So, x = 200. This means there are 200 people behind you in line.
To find the total number of people in line, we substitute the value of x back into the equation for the whole line:
Total number of people = 3x = 3 * 200 = 600.
Therefore, there are 600 people in line for concert tickets.
I hope this explanation helps! Good luck on your test, and remember to bring a few rubber chickens for extra luck! :)
To solve this problem, we will use algebraic expressions and equations. Here's a step-by-step explanation of how to solve it:
Step 1: Assign variables:
Let's assign "x" to represent the number of people behind you in line.
Step 2: Set up equations:
According to the problem, there are 200 more people ahead of you than behind you in line. So, the number of people ahead of you would be x + 200.
Furthermore, the whole line, which represents the total number of people in line, is three times the number of people behind you. So, the whole line can be represented as 3x.
Step 3: Create an equation:
To find the total number of people in line, we need to sum up the number of people ahead of you (x + 200) and the number of people behind you (x), since these two parts make up the entire line.
Therefore, the equation becomes: (x + 200) + x = 3x.
Step 4: Solve the equation:
Let's solve the equation to find the value of x.
By simplifying the equation: x + 200 + x = 3x becomes 2x + 200 = 3x.
Subtracting 2x from both sides gives us: 200 = x.
Step 5: Calculate the total number of people in line:
Now that we have found the value of x, substitute it back into one of the earlier equations to determine the total number of people in line.
Using the equation for the whole line, 3x, substitute x = 200: 3 * 200 = 600.
Therefore, there are 600 people in line for the concert tickets.
By following these steps, you should be able to solve similar problems that involve finding the value of unknown quantities. Good luck with your test!