Systems of equation

Question

A theater charges $60 per ticket for seats in section, $30 in section B and $10 in section C. For one play, 9500 tickets were sold for a total amount of $270,000 in revenue. If 500 more were sold then the other two sections combined, how many tickets in each section were sold? This is a system of three equations questions

Answer 1

Here are your first two formulas.

 

1] A + B + C = 9500

 

2] 60A + 30B + 10C = 270,000, or

6A + 3B + C = 27000

 

However, for the third one, you seem to be missing part of the sentence.  You say "If 500 more were sold then the other two sections combined."  500 of which section?

 

Ok, so if there were 500 more in section B than in the other two combined, your third formula is:

 

B = A + C + 500, or

 

3] - A + B - C = 500

 

If we add the first and third formulas, we get

2B = 10000, so B = 5000

 

So A + C = 4500, and C = 4500 - A

 

6A + 3B + C = 27000

6A + 15000 + 4500 - A = 27000

6A = 7500

A = 1250

 

And C = 3250

 

Hope this helps, Austin!