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At a college production of Evits, 500 tickets were sold. The ticket prices were $8, $10, $12, and the total income from ticket sales was $4700. How many tickets of each type were sold if the combined number of $8 and $10 tickets sold was 4 times the number of $12 tickets sold?

Respuesta :

sqdancefan

Let a, b, c represent the numbers of $8, $10, and $12 tickets sold, respectively. The problem statement gives rise to three equations:

  • a + b + c = 500
  • 8a +10b +12c = 4700
  • a + b - 4c = 0

Solving these equations by your favorite method gives ...

... (a, b, c) = (250, 150, 100)

250 $8 tickets, 150 $10 tickets, and 100 $12 tickets were sold.

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After you subtract the 3rd equation from the first to find 5c=500, you can substitute c=100 into the first two equations to get two equations in two unknowns. You know several ways to solve such equations, including elimination, substitution, and graphing, at least. Cramer's method is another viable choice.

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