Math Help - Word Problem. Can't figure out equation.

1. Word Problem. Can't figure out equation.

Need help figuring out the equation you'd get from the following paragraph...

A Broadway performance of The Phantom of the Opera had a paid attendance of 320 people. Balcony tickets cost 42$, and orchestra tickets cost 64$. Ticket sales receipts totaled 16,630$. How many tickets of each type were sold? I seem to have forgotten how I'd write this as an equation... I don't want to have the equation solved (yet, I'll see if I can get it on my own) but I've spent the last 20 minutes trying to find a way to make equations to help figure it out. I have to use a system of two linear equations to solve it, either addition method or substitution method. Thank you for any help. 2. Originally Posted by complicated A Broadway performance of The Phantom of the Opera had a paid attendance of 320 people. Balcony tickets cost 42$, and orchestra tickets cost 64$. Ticket sales receipts totaled 16,630$. How many tickets of each type were sold?
Try an online lesson to learn the general set-up for "mixture" word problems.

Once you've studied that, the following should make sense:

. . .tickets:
. . . . .total: 320
. . . . .balcony: b
. . . . .orchestra: 320 - b

. . .income:
. . . . .total: 16630
. . . . .balcony: 42b
. . . . .orchestra: ...

Complete the table. Add the incomes from the two types of tickets, and set equal to the given total income. Solve for the variable.

3. Originally Posted by stapel
Try an online lesson to learn the general set-up for "mixture" word problems.

Once you've studied that, the following should make sense:

. . .tickets:
. . . . .total: 320
. . . . .balcony: b
. . . . .orchestra: 320 - b

. . .income:
. . . . .total: 16630
. . . . .balcony: 42b
. . . . .orchestra: ...

Complete the table. Add the incomes from the two types of tickets, and set equal to the given total income. Solve for the variable.
Orchestra would be 16630 - 42b right?

But I don't know what b is and have no equation to figure out what b could be so I can't solve it this way, unless I'm just missing something. That site you linked to me didn't really help me understand it.

Edit: Hang on I might be getting it. bbiab

4. Does this look right?

let a = orchestra tickets sold
let b = balcony tickets sold

Tickets | $Tickets | Total 320 - a |$42 | $42(320 - a) - balcony a |$64 | \$64a - orchestra
320 | --------| 16630 - total

5. Lost again.

Managed to get this much...

42(320 - a) + 64a = 16630
13440 - 42a + 64a = 16630
13440 + 22a = 16630
22a = 3190
/22 = /22
a = 145

Where do I go from here though?

Edit:

Would I just take 320 - 145 = b?
That seems too easy to me but makes sense, any feedback is appreciated.

6. Yup. You've got it. To check your work, just make sure that

a + b = 320
and
42(320-a) + 64(a) = 16630

if a = 145, and b = 320-145 = 175
then 145 + 175 = 320
and
42(175) + 64(145) = 7350 + 9280 = 16630