Question 1189692

A stadium has 48000 seats. Seats sell for ​$35 in Section​ A, ​$30 in Section​ B, and ​$25 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 ​$1510500 from each​ sold-out event. How many seats does each section​ hold
<pre>With a 48,000-seat capacity, and with Section A's total capacity being that of both B and C, it's clear that <font color = red><font size = 4><b>
Section A's capacity</font></font></b>, as well as Sections B and C, combined, is:{{{matrix(1,3, "48,000"/2, "=", highlight("24,000"))}}}
Section A's capacity is 24,000, and with each seat selling for $35, proceeds from Section A = 35(24,000) = $840,000
As proceeds from Section A totals $840,000, proceeds from Sections B and C, combined = $670,500 ($1,510,500 - $840,000)

Let seating capacity in Section B, be B
As both Sections B and C have a capacity of 24,000, seating capacity in Section C = 24,000 - B
We then get: 30B + 25(24,000 - B) = 670,500
6B + 5(24,000 - B) = 134,100 ------ Factoring out GCF, 5
6B + 5(24,000) - 5B = 134,100
6B - 5B = 134,100 - 5(24,000)
Seating capacity in Section B, or B = 134,100 - 120,000 = <font color = magenta><font size = 4><b>14,100</font></font></b>
Seating capacity in Section C: 24,000 - 14,100 = <font color = magenta><font size = 4><b>9,900</font></font></b></pre>