Question

can you check my answer?

Answer 1

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 2

i think its 250

Answer 3

Please demonstrate your methodology.

Answer 4

25000 = 50X + (2)75X
25000 =200X
X = 125

Answer 5

Then do the ratio of 2:1

Front = 250
Back = 125

Answer 6

Hmmm... It seems a little magic. Translate the problem statement more directly.

F = # of seats in the front section
B = # of seats in the back section

Please provide clear and sufficient definitions. This will save you.

"The number of front section seats is twice the number of back section seats."

1) F = 2B

"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."

2) 50B + 75F = 25000

"How many seats are in the front section?"

Substitute from 1) into 2)

50B + 75(2B) = 25000

Solve and finish.

50B + 150B = 25000
200B = 25000
2B = 250
B = 125

Using Equation 1), we have: F = 2(125) = 250

Checking: 125(50) + 250(75) = 6250 + 18750 = 25000

You do have the correct answer, but the fact that you asked to have it checked suggests you are missing some confidence. Just be a little more deliberate. Use my work as an example of a clean, understandable, correct, and reproducible methodology that will build your confidence.