## kaylamalik_xo 3 years ago 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

1. dietrich_harmon

C

2. kaylamalik_xo

@dietrich_harmon how? ;o

3. geoffb

No kidding.

4. geoffb

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?

5. kaylamalik_xo

@geoffb So it really is C?

6. geoffb

Definitely not.

7. kaylamalik_xo

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

8. geoffb

Careful...

9. geoffb

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

10. kaylamalik_xo

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

11. geoffb

No, not 4x.

12. geoffb

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

13. kaylamalik_xo

-2x+1400=1340

14. geoffb

Yes, good.

15. kaylamalik_xo

x=30

16. geoffb

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.

17. geoffb

Does that make sense?

18. kaylamalik_xo

OH so its B

19. geoffb

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

20. kaylamalik_xo

thanks @geoffb

21. geoffb

You're welcome! :)