Question

An auditorium earned $25,000 in sold-out concert ticket sales. Front section tickets cost $75 per seat and back section tickets cost $50 per seat. The number of front section seats is twice the number of back section seats. How many seats are in the front section?

Answer 1

b = back section, f = front section

75f + 50b = 25,000
f = 2b

75(2b) + 50b = 25,000
150b + 50b = 25,000
200b = 25,000
b = 25,000/200
b = 125

f = 2b
f = 2(125)
f = 250

front section (f) = 250...back section (b) = 125

Answer 2

250 seats

Explanation:

Let b denote the back section seats

and f denotes the front section seats

Then, f = 2b

75f + 50b = 25,000

75(2b) + 50b = 25,000 (on putting f=2b)

⇒150b + 50b = 25,000

⇒200b = 25,000

⇒b = 25,000/200

⇒b = 125

f = 2b

⇒f = 2(125)

⇒f = 250

Hence, There are 250 seats in the front section