Let the price of the silver ticket be \( x \). Then, the price of the gold ticket will be \( x + 8 \).
Patrick bought 10 tickets of each type, so the total cost for the silver tickets is: \[ 10x \] and the total cost for the gold tickets is: \[ 10(x + 8) \]
The total cost can be expressed as: \[ 10x + 10(x + 8) = 140 \]
Now, let's simplify this equation: \[ 10x + 10x + 80 = 140 \] \[ 20x + 80 = 140 \]
Next, subtract 80 from both sides: \[ 20x = 140 - 80 \] \[ 20x = 60 \]
Now, divide both sides by 20: \[ x = 3 \]
So, the price of the silver ticket is \( 3 \) dollars. The price of the gold ticket is: \[ x + 8 = 3 + 8 = 11 \]
Thus, the prices of the tickets are:
- Silver ticket: \( \boxed{3} \) dollars
- Gold ticket: \( \boxed{11} \) dollars
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