Question 789804
A basketball team sells tickets that cost $10, $20, and VIP seats for $30. The team has sold 452 tickets overall. It has sold 87 more $20 tickets than $10 tickets. The total sales are $7650, how many tickets of each kind have been sold?

Ive been trying to put together an equation to figure this out but I just cant seem to figure it out. Could you please explain how I would put these into an equation? Thank you!


Let number of $10 and $30 tickets sold be C, and E, respectively


Then number of $20 tickets sold = C + 87


Therefore, C + C + 87 + E = 452 ------ 2C + E = 365 ----- eq (i)


Also, 10C + 20(C + 87) + 30E = 7,650 ----- 10C + 20C + 1,740 + 30E = 7,650 ----- 30C + 30E = 5,910 ------ 30(C + E) = 30(197)
C + E = 197 ------ eq (ii)


{{{system (2C + E = 365_________eq__(i), C + E = 197__________eq__(ii))}}}


C = 168 ------- Subtracting eq (ii) from eq (i)


C, or number of $10 tickets sold = {{{highlight_green(168)}}}


I'm sure you can find the number of $20 and $30 tickets sold.


After determining them, do a check!! 


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