Question

Tickets for a school play cost $5 if you buy them early, and $7 if you buy them the day of the show. If 200 tickets are sold, and the total amount of money from ticket sales was $1340, how many tickets were purchased early?
A. 170 tickets
B. 30 tickets
C. 100 tickets
D. 124 tickets

Answer 1

C

Answer 2

@dietrich_harmon how? ;o

Answer 3

No kidding.

Answer 4

Let early tickets be \(x\). Since there are 200 total, late tickets must be \(200 - x\).

You also know that the sum of all tickets is $1340. So:
\[5x + 7(200-x) = 1340\]
Does that make sense to you?

Answer 5

@geoffb So it really is C?

Answer 6

Definitely not.

Answer 7

I thought so @geoffb. I thought it was A.

Answer 8

Careful...

Answer 9

Did you work out the formula above? Does it make sense how I got it and what it means?

Answer 10

So Id end up with 4x+1400=1340?

Answer 11

No, not 4x.

Answer 12

\[5x + 1400 - 7x = 1340\]

Answer 13

-2x+1400=1340

Answer 14

Yes, good.

Answer 15

x=30

Answer 16

Very good!

So once you solve for x, a very important step is to go back and look at what you chose x to represent. In this case, we chose for it to represent tickets purchased early. If we had let it represent tickets purchased late, you would end up with x = 170, but the answer *wouldn't* be A, because it is looking for tickets purchased early, not late.

Answer 17

Does that make sense?

Answer 18

OH so its B

Answer 19

Yes, and you can test it if you want (I would if you were doing a test.

30 early tickets x $5 = $150
170 late tickets x $7 = $1190
Total ticket revenue = $1340

Answer 20

thanks @geoffb

Answer 21

You're welcome! :)