## JackieLe 3 years ago A team won 3 of their first 10 games. If they win the next n games, they will have won 50% of their games. What is the value of n?

1. JakeV8

Games played so far = 10 Games won so far = 3 % won so far = 30% Win the next 10 games: played 20, won 13, % won = 65% ( = 13/20) ... too much games won = 3 + n games played = 10 + n (3 + n) / (10 + n) = 50% = 1/2

2. JakeV8

So (3 + n)/(10 + n) = 1/2 --->> (3+n) = (1/2)(10+n) 3 + n = 10/2 + n/2 (1/2)n = 10/2 - 3 = 10/2 - 6/2 = 4/2 = 2 (1/2)n = 2 n = 4 CHECK: won 3 games out of 10, winning % = 30% Win next 4 games... total games won = 7, total games played = 14, win % = 7/14 = 50%

3. JakeV8

sorry for the initial mistake :)

4. JackieLe

Thanks! :)

5. JakeV8

Do you understand how to set it up?

6. JackieLe

No problem~

7. JakeV8

I kinda gave it to you, but it might be useful to see an example of how to set up a problem like this... you have to think through the plain language version of the word problem and translate into "math language".

8. JackieLe

Actually I don't get why its n+3 and n+10. How did that come t o set up that way and then divided?

9. JackieLe

Yeah, that the number one problem I have when facing math word problems.

10. JakeV8

if you win 4 games out of 8 played, you have a 50% win percentage, right? The way the problem was stated, you had already played 10 games, but you had only won 3. So, your coach said "go team" or whatever... and now you start winning every game. So after the next game, you have won 4 and played 11. Win % = 4/11 After the 2nd game, you have won 5 (or initial 3 + 2 more) & played 12. Win% = 5/12 After 3 more games, you have won 6 & played 13. Win % = 6/13 After 4 more games, you have won 7 & played 14... win % = 50%, finally!!!

11. JakeV8

about word problems, it gets easier with practice, trust me... just talk it out, either out loud (if you're alone :) ) or at least talk it out in your mind, and don't let yourself get all confused. It's tough at first, but you can learn it.

12. JakeV8

I like to think that word problems are the teacher's way of trying to "beat you" (as in win over you, not actually beat you...)... and your challenge in life is to get your mind around this stuff so they can't win :) There's often some trick or catch or whatever... once you learn to think like they think, they lose their "power" over you. (I know, it's cheesy, but it does seem to sorta describe the situation... don't let them win!!!) :)

13. JackieLe

Thank you! That really help explaining up somethings. I guess if I look it that way there is truth to that, huh. Practice makes perfect right? :)

14. JakeV8

Absolutely :) Glad to help :) It's easy to preach "practice makes perfect" but with these types of problems, it really does help. Just don't get discouraged, and certainly don't get "scared" (aaaack!!) of word problems :)