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?

Re: simultaneous equation problem

Quote:

Originally Posted by

**Mathshelp246** 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

Quote:

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,