The school that molly goes to is selling tickets to a choral performance. on the first day of ticket sales the school sold 6 senior citizen tickets and 7 student tickets for a total of 174$. the school took in $318 on the second school day by selling 10 senior citizen tickets and 14 students tickets. find the price of a senior citizen ticket and the price for a student ticket

The cost of a senior citizen ticket is $15 and the cost of a student ticket is $12.

How did I get this?
We know that 6 citizen tickets and 7 student stickers sold for $174 the first day. And 10 citizen tickets and 14 student tickets sold for $318 the second day.

1. create two equations out of this: C= citizen cost per ticket and S = student cost per ticket.

  6C + 7S = $174
10C + 14S = $318

2. Use process of elimination. Multiply the first equation by 2 because we want two variables to cancel out.

-12C - 14S = -$348
10C + 14S = $318
Combine like terms.

-2C = $30
Divide by -2 on both sides. The left side cancels out.

C = $30/-2
C = -$15 (In this case the negative doesn't matter)

C = $15 (cost of senior citizen ticket)

Plug the value of C into any of the two equations so we can get the value of S.

6($15) + 7S = $174
Distribute the 6 into the parenthesis.

$90 + 7S = $174
Subtract both sides by $90 and the left side will cancel out.

7S = $84
Divide both sides by 7.
S = $12

Student ticket: $12
Senior citizen ticket: $15

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