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)

Question

$blank for each silver ticket and $blank for each gold ticket

Answer 1

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

Patrick bought 10 tickets of each type, so the total cost for the silver tickets is:

\[ 10x \]

The total cost for the gold tickets is:

\[ 10(x + 8) \]

According to the problem, the total amount spent by Patrick is $140. Therefore, we can set up the equation:

\[ 10x + 10(x + 8) = 140 \]

Now, simplify the equation:

\[ 10x + 10x + 80 = 140 \] \[ 20x + 80 = 140 \]

Subtract 80 from both sides:

\[ 20x = 60 \]

Now, divide by 20:

\[ x = 3 \]

So, the price of a silver ticket is \( x = 3 \) dollars.

Now, we can find the price of a gold ticket:

\[ x + 8 = 3 + 8 = 11 \]

Therefore, the prices of the tickets are:

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

Final answer: $3 for each silver ticket and $11 for each gold ticket.