This is my question VVV

Question

Cowboy Stadium, home of the Dallas Cowboys of the NFL,
seats approximately 9800 more fans than does Candlestick
Park, home of the San Francisco 49ers. Soldier Field, home
of the Chicago Bears, seats 8700 fewer fans than Candlestick
Park. If the total seats in these three stadiums is 211,700,
how many seats are in each of the three stadiums?

Answer 1

Hello, Pamela

First, I am going to define the different variables.

Let x  be the Cow Boy Stadium 

Let y be the  Candle Stick Park

Let z  be Soldier Field

 

1) x= y+ 9,800          or  y= x- 9,800

2) z= y- 8,700           or   y= z+ 8,700

 

x= y + 9,800 tell us that Candle (y) has 9,800 fewer seats than Cowboy.  

 

z= y- 8,700  tells us that Soldier (z) has 8,700 fewer seats than Candle.

 

We are informed that the total number of seats in all three stadiums is 211, 700.

3) x+ y + z = 211, 700       Substituting and solving in terms of y.

(y+ 9,800)+ y+ (y - 8,700) = 211, 700        Combining like terms

                            3y+ 1,100= 211, 700      Subtracting 1,1000          

                                    -1,100   -1,100

                                          3y= 210,600     Dividing by 3

                                            y= 70, 200

So, if you plug in 70,200 for y in equations # 1 and # 2 above, you will get the values for x and y.  x, Cowboy, has 80,000 seats, y, Candle has 70, 200 seats and z, Soldier, has 61,500 seats.

 

Hey, if you think this is long, try to type it on an iPad mini with an attitude :(

 

I hope this will help you out.  

D.Y. T

 

 

 

 

 

 

Answer 2

Let x be seats of Cowboy Stadium

Let y be seats of Candlestick

Let z be seats of Soldier field

 

x + y + z = 211700        eq. 1

 

x = 9800 + y                  eq. 2

 

z = y - 8700                    eq. 3

 

substitute eq. 3 in to eq. 1:

 

x + y + (y - 8700) = 211700

 

x + 2y - 8700 = 211700

 

x + 2y = 211700 + 8700

 

x + 2y = 220400             eq. 4

 

substitute eq. 2 into eq. 4

 

 

 

(9800 + y) + 2y = 220400

 

9800 + 3y = 220400

 

3y = 220400 - 9800

 

y = 70200

 

let's use eq.2 to solve for x:

 

x = 9800 + 70200  =  80000

 

let's use eq. 3 to solve for z:

 

z = 70200  - 8700 = 61500

 

so x = 80000, y = 70200, and z = 61500

 

 

 

 

Answer 3

Let Candlestick park stadium capacity be x, since we are comparing the other stadium capacities to this one

 

Then Cowboy stadium capacity would be Candlestick capacity + 9800, or x+9800

 

And Soldier Field would be Candlestick capacity - 8700, or x - 8700

 

The sum of the stadiums seat 211,700, or Candlestick + Cowboy Stadium + Soldier Field = 211,700

 

So:

 

x + (x+ 9800) + (x -8700) = 211,700

 

Solve:

 

3x + 1100 = 211,700

 

x = 70,200 = Candlestick capacity

 

Now just use the information to find the other two stadium capacities and you're done.