A basketball team sells tickets that cost​ \$10, \$20,​ or, for VIP​ seats,​ \$30. The team has sold 3237 tickets overall. It has sold 183 more​ \$20 tickets than​ \$10 tickets. The total sales are ​\$60,750. How many tickets of each kind have been​ sold?

How many \$10 tickets?

How many \$20 tickets?

How many \$30 tickets?

Relevance
• x = # \$10 tickets

y = # \$20 tickets

z = # \$30 tickets

x + y + z = 3237

y - x = 183 or x = y - 183

so 2y + z = 3420 ...... add these two equations together

10*x + 20*y + 30*z = 60750 .......... the dollar amounts

==> 10(y - 183) +20y + 30z = 60750

==> 30y + 30z = 60750 + 1830

==> y + z = 2025 + 61

==> y + z = 2086

==> y = 3420 - 2086 = 1334

hence z = 2086 -1334 = 752

and x = 1334 - 183 = 1151

so 1151 \$10 tickets

and 1334 \$20 tickets

and 752 \$30 tickets

total 3237 tickets.... (check)

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• \$10 x 1,151 = \$11,510

\$20 x 1,334 = \$26,680

\$30 x 752 = \$22,560

1,151 + 1,334 + 752 = 3,237 tickets sold

\$11,510 + \$26,680 +\$22,560 = \$60,750

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• 10x+20y+30z = 60750

x+y+z = 3237

y = x + 183

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