Online concert tickets cost $37 each, plus a service charge of $8.50 per ticket. The Web site also charges a transaction fee of $14.99 for the purchase. You paid $242.49. How many tickets did you
buy?
Let x be the number of tickets bought.
The cost of each ticket without the service charge is $37.
The total cost of the x tickets is 37x dollars.
The service charge for each ticket is $8.50.
The total cost of the service charge for the x tickets is 8.50x dollars.
The transaction fee is $14.99.
The total cost of the transaction fee and the tickets is 37x + 8.50x + 14.99 = $242.49
Combining like terms, we get 45.50x + 14.99 = $242.49
Subtracting 14.99 from both sides, we get 45.50x = $227.50
Dividing both sides by 45.50, we get x = 5
You bought 5 tickets. Answer: \boxed{5}.
9a. Solve:
-x+1+5x=2+4x+9
9b. solve
-2x+7+8x=2+6x+5
9a.
To solve the equation -x + 1 + 5x = 2 + 4x + 9, we can start by simplifying both sides of the equation:
-x + 1 + 5x = 2 + 4x + 9
Rearranging the terms:
- x + 5x - 4x = 2 + 9 - 1
Combining like terms:
x = 10
Therefore, x = 10.
9b.
To solve the equation -2x + 7 + 8x = 2 + 6x + 5, we can start by simplifying both sides of the equation:
-2x + 7 + 8x = 2 + 6x + 5
Combining like terms on both sides:
(8x - 2x) + 7 = (6x + 2 + 5)
6x + 7 = 6x + 7
Notice that both sides of the equation are identical. The equation is an identity and holds true for all real values of x. Therefore, there is no unique solution for this equation.
To determine the number of tickets you purchased, we can work backwards by subtracting the extra charges from the total price you paid.
Let's start by subtracting the transaction fee from the total price:
Total price - Transaction fee = Amount for tickets
$242.49 - $14.99 = $227.50 (Amount for tickets)
Now, let's figure out the cost of each ticket without the service charge:
Amount for tickets / (Ticket price + Service charge) = Number of tickets
$227.50 / ($37 + $8.50) = Number of tickets
$227.50 / $45.50 = Number of tickets
Number of tickets = 5
Therefore, you purchased 5 tickets.