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.