There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.(1 point)

$__ for each silver ticket and $__ for each gold ticket

1 answer

Let the price of the silver ticket be \( x \). Then, the price of the gold ticket would be \( x + 8 \).

Patrick bought 10 tickets at each level, so he bought:

  • 10 silver tickets for \( 10x \)
  • 10 gold tickets for \( 10(x + 8) \)

The total amount spent on tickets can be expressed as: \[ 10x + 10(x + 8) = 140 \]

Now, simplify the equation: \[ 10x + 10x + 80 = 140 \] \[ 20x + 80 = 140 \]

Subtract 80 from both sides: \[ 20x = 60 \]

Divide both sides by 20: \[ x = 3 \]

Now we have the price of the silver ticket. To find the price of the gold ticket: \[ x + 8 = 3 + 8 = 11 \]

Thus, the price of each ticket is:

  • Silver ticket: $3
  • Gold ticket: $11

Final answer: Silver ticket: $3, Gold ticket: $11.