solving systems with three variables Algebra II help?.?

i don't need it worked out or anything. just set up the system.

A Stadium has 49,000 seats. Seats sell for $25 in section A, $20 in section B, and $15 in section C. The number of seat in section A equals the total number of seats in Sections B and Section C. Suppose the stadium takes in $1,052,000 from each sold-out event. How many seats does each section hold?

Update:

thanx you so much! i really wish i understood this Alg stuff. i'm better with geomerty.

4 Answers

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  • 1 decade ago
    Best Answer

    Describing revenue:

    25A+20B+15C=1,052,000

    Describing available seats:

    A+B+C=49,000

    Describing the relationship between number of seats:

    A= B+C

    or...

    B+C-A=0

    So those are your three equations.

  • 1 decade ago

    Let:

    a = seats in section A

    b = seats in section B

    c = seats in section C

    a = b + c (1)

    25a + 20b + 15c = 1052000 (2)

    a + b + c = 49000 (3)

    Those are your three equations

    Substitute (1) into (3)

    a + a = 49000

    2a = 49000

    Therefore a = 24500

    Substitute a into (1) and (2)

    b + c = 24500 (4)

    25(24500) + 20b + 15c = 1,052,000

    612500 + 20b + 15c = 1,052,000

    20b + 15c = 439,500 (5)

    I have now created a system of two equations which will allow me to find b and c

    Make b the subject in (4)

    b = 24500 - c

    Substitute b into 5

    20(24500 - c) + 15c = 439,500

    490,000 - 20c + 15c = 439,500

    -5c = -50,500

    c = 10,100

    Therefore

    b + c = 24500

    b + 10,100 = 24500

    b = 14400

  • mehan
    Lv 4
    3 years ago

    permit: 2x - 3y + z = 6 (First Equation) x - y + z = 2 (2nd Equation) x - y - 2z = 8 (0.33 Equation) Then; Subtract equation 2 from equation 3 subsequently, (x - y - 2z = 8) - (x - y + z = 2) ______________ -3z = 6 z = -2 (answer) Subtract equation 2 from equation a million (2x - 3y + z = 6) - (x - y + z = 2) ______________ x - 2y = 4 x = 4 + 2y (equation 4) evaluate equation 2...then replace the values of z and x. x - y + z = 2 4 + 2y - y + (-2) = 2 y = 0 (answer) evaluate equation 4..then replace the cost of y x = 4 + 2(0) x = 4 (answer) good luck!

  • 1 decade ago

    Here it is...

    A + B + C = 49,000

    25A + 20B +15C = 1,052,000

    A = B + C

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