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        riddles >> putnam exam (pure math) >> How do you solve? 
        
(Message started by: Bamaboys on Sep 7^th, 2006, 8:18pm)

Title: How do you solve?
Post by Bamaboys on Sep 7^th, 2006, 8:18pm

This math problem has been bugging me for a while now. Here it is:

900-8(5-2) / 3(15-10)

Note that after each parentheses there should be a squared sign, but I don't know how to make that on a computer. :'(Also, the / means divide. The answer is supposed to be 300, but I can't figure out how. I've done the problem everyway I know, and can't figure out 300 as a solution.
Help!!

Please... :)

Title: Re: How do you solve?
Post by towr on Sep 8^th, 2006, 12:30am

Let's first write the missing squares (btw, if you click quote, you can see how I make those)
900-8*(5-2)² / 3*(15-10)²

Now, to calculate the value, it is important to realize the order of operations.
First calculate things in parenthesis. These have the highest priority
900-8*3² / 3*5²

Next highest priority are powers (in this case just the squares, but also cubes or higher or lower powers)
900-8*9 / 3*25

Next come multiplications and divisions. I suspect this is where it might go wrong for you. Multiplication and division have the same priority, this means you must apply them as they come, from left to right. Don't first do all multiplication, and then the divisions, or vice versa, but take them as they come
So
900-72 / 3*25
900-24*25
900-600

Next come addition and subtraction, again they have the same priority and you take them as they come; but since we only have a subtraction left there's no problem.
We get
300

Title: Re: How do you solve?
Post by Bamaboys on Sep 8^th, 2006, 2:05pm

Thank you! Alot! Yes, the multiplying/dividing was what messed me(and 11 other people who tried to solve this) up. I feel pretty stupid now that I realise how to solve it. And again, thanks.

Title: Re: How do you solve?
Post by Icarus on Sep 8^th, 2006, 4:56pm

on 09/08/06 at 14:05:28, Bamaboys wrote:

I feel pretty stupid now that I realise how to solve it.

I have a doctorate in mathematics, but I still remember the first time I ran into the question of order of operations. I proudly picked the wrong answer in a classroom discussion and was contemptuous (fortunately, only in my own head) of those who disagreed.:-[ Sometimes eating crow is the best diet one can have.

[Cultural reference: "Eating crow" means having to admit you got it wrong.]

Title: Re: How do you solve?
Post by Bamaboys on Sep 9^th, 2006, 5:25pm

Hate to keep bumping this thread, but the test is Moday, and there's one more problem I can't figure out.

2/5(-30)(1/3) - 2/5 - (-30) - 1/3

The answer is supposed to be 32 4/15. I'm probably just making stupid mistakes or overlooking something obvious, like in the first one. Oh, and the / in this one means fractions, not divide.

Title: Re: How do you solve?
Post by Icarus on Sep 9^th, 2006, 6:04pm

Fractions ARE division, but I assume what you mean is that 2/5(-30)... means (2/5)*(-30) and not 2/(5*-30), which is what it should mean as you've expressed it.

Either way, though, you've either miscopied the problem or the answer you are looking for is wrong. Every term in there is negative except the - (-30), which is positive. So you have 30 up, and everything else subtracts from it. That means the total is going to be less than 30, whereas 32 4/15 > 30.

Please double check the problem to make sure you have it copied right.

Title: Re: How do you solve?
Post by Bamaboys on Sep 9^th, 2006, 6:13pm

The problem was copied right, but maybe I couldn't figure out 32 4/15 for the answer because the teacher gave us the wrong one. Thanks alot.

Title: Re: How do you solve?
Post by Icarus on Sep 9^th, 2006, 6:23pm

Assuming I am correct about it needing to be

(2/5)(-30)(1/3) - (2/5) - (-30) - (1/3)

Then the answer is 379/15 = 25 4/15.

Title: Re: How do you solve?
Post by Bamaboys on Sep 9^th, 2006, 6:33pm

on 09/09/06 at 18:23:06, Icarus wrote:

Assuming I am correct about it needing to be

(2/5)(-30)(1/3) - (2/5) - (-30) - (1/3)

Then the answer is 379/15 = 25 4/15.

You would be correct in assuming that. That was the answer I kept coming up with, so I guess the teacher just made a mistake. Thanks again