Short math quadractic equation word problem*best answer?
josh buys concert tickets worth $180, he then keeps 2 of the tickets and sells the rest for 9 dollars more, he make a total profit of $36, after selling all the tickets.
what was the original ticket price?
solve
(x-2)(180/x + 9) - 180 = 36
To solve this problem, let's break it down step by step:
1. Let's say the original ticket price is x dollars.
2. Josh buys a certain number of tickets, which total $180. Since the price of each ticket is x dollars, we can set up the equation: x * (number of tickets) = 180.
3. We know that Josh keeps 2 tickets, so the number of tickets he sells is (number of tickets) - 2. We can substitute this value into our equation: x * ((number of tickets) - 2) = 180.
4. Josh sells the remaining tickets for $9 more than the original price, so the selling price per ticket is (x + 9) dollars. The total profit from selling the remaining tickets is $36. Using the selling price and the number of tickets sold, we can set up another equation: (x + 9) * ((number of tickets) - 2) = 180 + 36.
5. Now we have two equations:
- x * ((number of tickets) - 2) = 180
- (x + 9) * ((number of tickets) - 2) = 216
6. From the first equation, we can isolate the number of tickets: (number of tickets) = 180 / x + 2.
7. Substitute this value into the second equation: (x + 9) * (180 / x) = 216.
8. Simplify the equation: (180x + 18x) / x = 216.
9. Multiply both sides by x to eliminate the fraction: 198x = 216x.
10. Subtract 198x from both sides to isolate x: 216x - 198x = 0.
11. Simplify: 18x = 0.
12. Divide both sides by 18: x = 0.
13. However, a ticket price of $0 does not make sense, so there is no solution for x.
Therefore, there seems to be an error or inconsistency in the problem statement or the calculations provided.