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 answer

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