Wednesday, July 27, 2011

Solution for free throws, Problem for probability

Thanks everyone for trying out the problem, and congrats to those who got the problem right!

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?

Solution:
First of all, we will need to set up a system of equations to solve this problem. Let's make x= # of free throws, y= # of two-point shots, and z= # of three-point shots. Now, we have x + 2y + 3z = 61. If they scored as many points with two-point shots as three-point shots, then 2y=3z. Their number of successful three throws was one more than their number of successful two-point shots, which means x = y + 1. Now we can substitute these into the original equation.

x + 2y + 3z = 61
(y + 1) + 2y + (2y) = 61
y + 1 + 2y + 2y = 61
5y + 1 = 61
5y = 60
y = 12

We can now plug in 12 in for y into x = y + 1 to solve for the number of free throws.

x = y + 1
x = 12 + 1
x = 13

The answer is 13 free throws.

Here's the next problem
Problem:
A pair of standard 6-sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference.

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


22 comments:

  1. Awesome it is always great to have a math refresher.

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  2. You remind me of my math teachers when I use to study in my former country. We always do these equations without calculator. But now I can't remember anything about it anymore lol. Thanks for reminding me.

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  3. gonna be visiting repeatedly to make sure i don't lose it before i go back to school :D

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  4. I am a bit confused, damnit!

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  5. I think I've heard the one you posted today, so I might actually try it haha

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  6. I think I need sleep...my brain is refusing to work at the moment...

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  7. Confused. That's what I am right now.
    But I'll come back to see the answer.

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  8. Woah, really interesting. I haven't focused that hard on math in a long time. You do a public service of keeping people like me from sliding into apathy for math. Still working on it, i need a pen and paper.

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  9. MAH BRAIN. OWOWOWOWOWOWOWOW...

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  10. I left school because of things like this hahaha

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  11. I'm really good at math and this stuff really confused me, nice blog choice.
    +Follow

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  12. should have listened more in school...:p

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  13. really interesting but also just a little above my head!
    +followed

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  14. awesome blog man

    following you now

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  15. reading that was like a psychological attack D:
    *followed*

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  16. free throws? basketball? this whole post went way over my head.

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  17. Damnit. I am not able to do this without a calculator, but I am not one to break rules, so I will not figure this out.

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  18. Awesome blog dude. I'm really into this sort of thing!

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