Question

stadium has 49,000 seats. Seats sell for ​$42 in Section​ A, ​$36 in Section​ B, and ​$30 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 ​$1,849,800 from each​ sold-out event. How many seats does each section​ hold?

Answer 1

Congrats on getting that far!

From here, simplify the equation by dividing each term by the greatest common factor: 6.

36B + 30C = 822600 becomes 6B + 5C = 137100

Now you have stackable simultaneous equations that you can easily work with:

6B + 5C = 137100

B + C = 24500

Multiply the terms in the second equation by either 6 or 5 so that you can subtract the second equation from the first equation and cancel out the B or C, respectively.

Example:

6B + 5C = 137100

minus 5B + 5C = 122500

equals B = 14600

Then plug your answer into the B + C = 24500 equation to find C.

Finally plug B and C into the A + C + B = 49000 equation to get A.