Let's define the price of the silver ticket as \( x \). Then, the price of the gold ticket would be \( x + 8 \) since the gold tickets are $8 more than the silver.
Patrick bought 10 tickets of each type, so:
- The total cost for silver tickets is \( 10x \).
- The total cost for gold tickets is \( 10(x + 8) \).
According to the problem, the total amount spent on the tickets is $140, so we can set up the following equation:
\[ 10x + 10(x + 8) = 140 \]
Now, simplify the equation:
\[ 10x + 10x + 80 = 140 \]
Combining like terms gives:
\[ 20x + 80 = 140 \]
Next, we can subtract 80 from both sides:
\[ 20x = 60 \]
Now, divide by 20 to solve for \( x \):
\[ x = 3 \]
So the price of the silver ticket is \( 3 \) dollars. To find the price of the gold ticket, we add 8:
\[ x + 8 = 3 + 8 = 11 \]
Thus, the prices of the tickets are:
- Silver ticket: $3
- Gold ticket: $11
In summary:
- Price for each silver ticket: $3
- Price for each gold ticket: $11
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