The school that Adam goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 5 senior citizen tickets and 15 student tickets for a total of $137.50. The school took in $430 on the second day by selling 20 senior citizen tickets and 44 student tickets. Find the price of a student ticket.

Let the price of one senior citizen ticket be sc and the price of one student ticket be st.

Let's write equations using the information given and the variables above:

=> 5sc + 15st = $137.50

=> 20sc + 44st = $430

Hmm.. We can multiply 5sc by 4 to get 20sc.

=> 4(5sc) + 4(15st) = 4($137.50)

=> 20sc + 60st = $550

Now we can subtract the second equation from the first to determine the price of a student ticket.

  20sc + 60st = $550

-  20sc + 44st = $430

=> 16st = $120

=> st = $7.5

So, the price of a student ticket is $7.5.

answer: the common difference is -0.10

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