student tickets to the school musical cost $3 each. All other tickets cost $5 each. Suppose that 272 tickets were sold for a total of $1120. How many tickets of each type were sold?

Answer 1

first we represent unknowns with variables.
let x = number of $3-tickets
since the total number of tickets ($3 and $5) is equal to 272,
let 272-x = number of $5-tickets
then we set-up the equation. to get the total cost, we multiply each price of the ticket with their number. thus,
3x + 5(272-x) = 1120
3x + 1360 - 5x = 1120
3x - 5x = 1120 - 1360
-2x = -240
x = 120 (number of $3-tickets)
272-x = 152 (number of $5-tickets)

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