Let's denote the price of a silver ticket as \( S \) dollars. According to the problem, the price of a gold ticket would then be \( S + 8 \) dollars.
Patrick bought 10 silver tickets and 10 gold tickets, spending a total of $140. We can set up the following equation based on this information:
\[ 10S + 10(S + 8) = 140 \]
Now, simplify the equation:
\[ 10S + 10S + 80 = 140 \]
Combine like terms:
\[ 20S + 80 = 140 \]
Now, subtract 80 from both sides:
\[ 20S = 140 - 80 \] \[ 20S = 60 \]
Now, divide both sides by 20:
\[ S = \frac{60}{20} = 3 \]
So, the price of a silver ticket is \( S = 3 \) dollars. Now, we can find the price of a gold ticket:
\[ \text{Price of gold ticket} = S + 8 = 3 + 8 = 11 \]
Therefore, the prices of the tickets are:
- Silver ticket: \( 3 \) dollars
- Gold ticket: \( 11 \) dollars