Question

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)
$ for each silver ticket and $ for each gold ticket...../...../............

Answer 1

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