multi step equation

Question

A total of 119 golden tickets were sold for an NBA match. A hundred general tickets and 6 platinum tickets were also sold. The price of a general ticket was three-fourth the cost of the golden ticket. The price of a platinum ticket was twice that of the golden ticket. How much was a golden ticket priced at, if the total collection from ticket sales was $6,592?

Answer 1

Hi Jeff, let gold represent the golden tickets. Let genl represent the general tickets. Let plat represent the platinum tickets. Set up an equation representing all of the tickets.

Equation to solve:

119 * gold + 100 * genl + 6 * plat = 6592

Given:

1 genl = 3/4 gold, 100 general tickets equals 75 golden tickets

1 plat = 2 gold, 6 platinum tickets equals 12 golden tickets

Substitute in equation to solve:

119 * gold + 3/4 * (100 * genl) + 2 * (6 * plat) = 6592

119 * gold + 75 gold + 12 gold = 6592

206 * gold = 6592

Divide both sides by 206

1 golden ticket = 32

The cost of 1 golden ticket is $32.00

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