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Math Help - simultaneous equation problem

  1. #1
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    simultaneous equation problem

    A concert hall has a inner and outer section.
    The inner section has seats arranged in rows of 40 and tickets in this section cost $140 ea
    The outer section has seats arranged in rows of 70 and tickets in this section cost $60 ea
    There are 10 more rows in the inner section than that of the outer section
    The seating capacity of the hall is 7000

    Using the information given- form equations for the seating capacity for the concert hall?

    This is an annoying maths question
    Thinking equation
    1. 40x+70y=7000
    2. 40x+10=70y-10 => 70y-40x=20?
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  2. #2
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    Re: simultaneous equation problem

    Quote Originally Posted by Mathshelp246 View Post
    A concert hall has a inner and outer section.
    The inner section has seats arranged in rows of 40 and tickets in this section cost $140 ea
    The outer section has seats arranged in rows of 70 and tickets in this section cost $60 ea
    There are 10 more rows in the inner section than that of the outer section
    The seating capacity of the hall is 7000

    Using the information given- form equations for the seating capacity for the concert hall?

    This is an annoying maths question
    Thinking equation
    1. 40x+70y=7000
    That makes no sense because you have not said what "x" and "y" represent.
    Assuming you mean that x is the number of rows of seats at $140 each andy is the number rows of seats sold at $60 each,
    then 40x+ 70y is the total number of seats so, yes, 40x+ 70y= 7000

    2. 40x+10=70y-10 => 70y-40x=20?
    No, this is not correct. With x the number of rows of seats in the first section, and y the number of rows of seats in the other section, the fact that "There are 10 more rows in the inner section than that of the outer section" tells us that x= y+ 10. Because there are 10 more rows rather than seats, we do NOT multiply by the number of seats per row and we do not have the "10" on both sides of the equation,
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