Matrix worded question

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Matrix worded question

An amphitheater has three sections. It charges $75 , $55 and $ 30 for each seat in each of
sections A, B and C respectively. There are three times as many seats in section A as in
section B. Additionally the total revenue for the 23000 seats in the venue is $870000.
Formulate the information and determine the number of seats in each section.
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Re: Matrix worded question

This post was updated on .
x = number of seats in section B
3x = number of seats in section A   ← there are 3 times as many seats in A as in B
23,000 - 4x = number of seats in Section C   ← there are 23,000 total seats

55(3x) + 75(x) + 30(23,000 - 4x) = 870,000  ← price per seat times number of seats equals total revenue
165x + 75x + 690,000 - 120x = 870000   ← multiplied / distributive property
240x + 690,000 = 870,000   ← combined like terms
-120x = -180,000  ← subtracted 690,000 from each side
x = 1500   ← divided each side by -120
3x = 4500   ← substituted 1500, in for x, into 3x
23,000 - 4x = 17,000   ← substituted 1500, in for x, into 23,000 - 4x

Section A = 4500 seats
Section B = 1500 seats
Section C = 17,000 seats

- Proof