Sunday, July 24, 2011

Solution for the maximum value, Problem for free throws

Thanks everyone for trying out the problem and posting in the comments! I'll try to put up a little easier problem this time.

Problem:
Suppose that |x + y| + |x - y| = 2. What is the maximum possible value of x^2 - 6x + y^2?

Solution:
When you first look at x^2 - 6x + y^2 you'll realize that if you want the maximum value, x would have to be a negative number to cancel out the -6x. Also, for the equation to be the maximum value, x and y would have to be the greatest absolute value possible. 

From the equation |x + y| + |x - y| = 2, you can see that |x + y| and |x - y| has to be less than 2. Basically, from looking at the problem for a bit, you can see that if x=-1 and y=1 the equation works.

|x + y| + |x - y| = 2
|-1 + 1| + |-1 - 1| = 2
|0| + |-2| = 2
|-2| = 2
2 = 2

If you plug in -1 for x and 1 for y into  x^2 - 6x + y^2 you get 8 which is the answer. 

Problem:
The players on a basketball team made some three-point shots, some two-points shots, and some one-point free throws. They scored as may points with two-points shots as with three-points shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws did they make?

Good luck! and remember calculators are not allowed. :)

30 comments:

  1. its time to brush up my math skills :)

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  2. oh i hate word problems! haha...but math is pretty cool.

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  3. This is just to much to handle xD

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  4. Ugh, word problems suck and I forgot to do yesterday's because I was busy. I'll try to get this one done tonight

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  5. 3 point shots: 2x, 2 point shots: 3x, 1 free throws: 3x+1.

    (2x x 3) + (3x x 2) + (3x+1) = 61

    6x + 6x + 3x + 1 = 61

    x = 4, 24 + 24 + 12 + 1. I WIN! NIGGAZ.

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  6. I'm a writer, my friend. Math is far, FAR beyond me.

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  7. If I was good at math, I'd not being blogging haha. "Tried" this one, but I guess I'm far from the right result.

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  8. I cheated! I used a calculator. I couldn't take the guilt.

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  9. Haha seems someone has already beat me to the answer! Guess I should read the comments before I crack out the pen and paper!

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  10. Interesting subject for a blog, I'm taking further maths at English A level next year, so I'm definitely going to follow/support this and see what happens

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  11. At first I was ready to break out a pencil and paper (ok, a calculator really) but then I saw the answer in the comments :P

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  12. Hahaha, pretty nice post. I think I know where am I supposed to go when I have a math problem. haha

    Keep doing it, nice blog!
    add

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  13. My brain just went crazy with so many #'s lol

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  14. I have a feeling im going to love this blog. Followed :)

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  15. 420 freeshots?

    i dunno im just guessing... and thats my default answer ;)

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  16. I think you're the best math poster on blogger. good job!

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  17. god, i remember that back from school :D
    +1

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  18. I worked it out in my brain in about 2 minutes using 10's as a starting point. I came up with eleven made free throws.

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  19. Lol i was never good at this kind of things.Maybe you will clear me out.Followed!

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  20. omg, ok now try to solve this:

    The mother is 21 years older than the daugter and in 6 years the mother will be 5 times older than the daugter!
    Question: Where is the Father?

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  21. I'm with the guy who commented earlier, his answer looks right to me.

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  22. unfortunately i looked at the comments before i started thinking about it so the next time i will do it as there was no sense in doing it now but also great blog mate cant wait for another problem.

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  23. i kinda ditched maths :P will be interesting to read though

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