Question

Lynn paid a total of $2,780 for 261 tickets to the theater. Student tickets cost $10 and adult tickets cost $15. How many student tickets and how many adult tickets did Lynn buy?

(I don’t need the answer but I saw this question earlier on here and the answer provided was incorrect!)

Answer 1

Lynn bought 227 student tickets and 34 adult tickets, spending a total of $2,780 for 261 theater tickets.

Let's use a system of equations to represent the given information. Let \(s\) represent the number of student tickets and \(a\) represent the number of adult tickets. The total number of tickets is 261, so we have the equation:

`\[s + a = 261\]`

Additionally, we know that the total cost of the tickets is $2,780, and the cost of a student ticket is $10, while the cost of an adult ticket is $15. Therefore, the second equation is:

`\[10s + 15a = 2780\]`

Now, we can solve this system of equations simultaneously. Let's first solve the first equation for one of the variables, say \(s\):

`\[s = 261 - a\]`

Now, substitute this expression for \(s\) into the second equation:

`\[10(261 - a) + 15a = 2780\]`

Distribute and simplify:

`\[2610 - 10a + 15a = 2780\]`

Combine like terms:

`\[5a = 170\]`

Divide by 5:

`\[a = 34\]`

Now that we know the number of adult tickets (\(a = 34\)), substitute this value back into the first equation to find the number of student tickets:

`\[s + 34 = 261\]`

`\[s = 227\]`

So, Lynn bought 227 student tickets and 34 adult tickets.