SOLUTION: Solving Linear Equations: You are selling tickets for a high school play. Student tickets cost $4 and general admission tickets cost $6. You sell 525 tickets and collect $2,876.

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Question 131557This question is from textbook
: Solving Linear Equations:
You are selling tickets for a high school play. Student tickets cost $4 and general admission tickets cost $6. You sell 525 tickets and collect $2,876. How many of each type of ticket did you sell.


First I said x = student tickets and y = general admission tickets, but then I got lost. This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Perfectly good start:

x = the NUMBER of student tickets
y = the NUMBER of GA tickets

And we know that x%2By=525 (First equation)

Since student tickets cost $4, the total amount of money collected from the sale of student tickets must be 4 times the number of student tickets, i.e., 4x.

Likewise, the total money collected from general admission tickets must be 6y.

And since those were the only two types of tickets sold, these two expressions must add up to the total amount of money collected, or:

4x%2B6y=2876 (Second equation)

Let's solve this by elimination.

Multiply the first equation by -4:
-4x-4y=2100

Now add this new equation term-by-term to the second equation:
%28-4x-4y%29=-2100 + 4x%2B6y=2876 = 0x%2B2y=776

2y=776
y=388

388 general admission tickets.

Go back to the original first equation and multiply by -6, then add term-by-term to the second equation:
-6x-6y=-3150 + 4x%2B6y=2876 = -2x%2B0y=-274

-2x=-274
x=137

137 student tickets.

Check:
388 + 137 = 525

388 * 6 = 2328
137 * 4 = 548

2328 + 548 = 2876. Answer checks.