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A stadium has 51,000 seats. Seats sell for ​$30 in Section​ A, ​$24 in Section​ B, and ​$18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in ​$1 ,310,400 from each​ sold-out event. How many seats does each section​ hold?

Respuesta :

Diatonic254

Section C = 11,100 seats

Section B = 14,400 seats

Section A =  25,500 seats

Step-by-step explanation:

  • We can develop 2 equations from the question;
  • We can assign the number of seats in section B as x while the number of seats in section C as y. Section A has x+y number of seats. Therefore;

(x + y ) + x + y = 51,000

x + y  + x + y = 51,000

2x + 2y = 51,000

2(x+y) = 51,000

X+y = 51,000 / 2

X + y = 25,500

  • The second equation about prices is;

30 (x + y) + 24x + 18y = 1,310,400

30x + 30y + 24x + 18y = 1,310,400

54x + 48y = 1,310,400

6 (9x + 8y) = 1,310,400

9x + 8y = 1,310,400 / 6

9x + 8y = 218,400

  • Now we have two equations that we can use to find the unknown values of x and y

9x + 8y = 218,400

-

9(x + y = 25,500)

=

9x + 8y = 218,400

-

9X + 9y = 229,500

=

-y = - 11, 100

Y = 11, 100

X = 25,500 – 11,100 = 14,400

Section C = 11,100

Section B = 14,400

Section A = 11,100 + 14,400 = 25,500

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beritop1089

Answer:

Step-by-step explanation:

Total seats = 51,000

Price per section;

A= $30

B= $24

C= $18

Number of seats;

If A = B+C

30(B+C)+24B+18C = $1,310,400

A+B+C=51000

replace A with (B+C)

(B+C)+B+C = 51000

2B+2C=51000

2B=51000-2C

B=[tex]\frac{51000-2C}{2}[/tex]

Therefore, B= (25500-C)

Next, solve the equation below to its simplest form;

30(B+C)+24B+18C = $1,310,400

30B+30C+24B+18C = $1,310,400

54B+48C= $1,310,400 and

now replace B with (25500-C) and solve for C

54(25500-C)+48C = $1,310,400

1,377,000-54C+48C = $1,310,400

1,377,000 - 1,310,400 = 54C- 48C

66,600= 6C

C = 11,100 seats

Plug in 11,100 in equation B= (25500-C) and solve for B;

B=25500-11,100

B = 14,400 seats

Next, this equation "A = B+C" to solve for A

A= 14,400 + 11,100 = 25,500

A=25,500 seats

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