Lenny Conundrum 208

[TDG]

Its a little late, but none the less

While exploring through the trading post, you find someone offering a Ghostkerbomb. When you ask what she wants for it, this is her reply:

"Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole number, and that's my price."

How much does she want for the Ghostkerbomb?

I'd start by saying

Let X = the Small Number
Let Y = the Larger Number

[Rachel]

thats what i did too, but i used a and b

[Siouxper]

I'm not a genius, so I just did trial and error. And once I got to several decimal places, I just entered my answer based on that. That'd be nice if there was a program for this, but then it'd be too easy

[shinigami1190]

lol, well i got my answer as well, heres what i did..
a-b=12
a*b=17

thus:
a=b+12

and because of that...
(b+12)b=17... which can be written as b(b+12)=17

from there.. i just did guess and check lol

[AySz88]

I'm not a genius, so I just did trial and error. And once I got to several decimal places, I just entered my answer based on that. That'd be nice if there was a program for this, but then it'd be too easy

Excel can help seek your goal, but Google's Calculator works fine if you know your formulas (or the completion of a certain square).

[gilbil]

Did you get a 4 digit number?[/url]

[Siouxper]

I'm not a genius, so I just did trial and error. And once I got to several decimal places, I just entered my answer based on that. That'd be nice if there was a program for this, but then it'd be too easy

Excel can help seek your goal, but Google's Calculator works fine if you know your formulas (or the completion of a certain square).

Excel 2003 is not my kind of software. I just can't use it correctly.

[AySz88]

Now that it's over, I'd better clarify:

"Excel can help seek your goal" = the "Goal Seek" feature of Excel
"know your formulas" = the quadratic formula
"completion of a certain square" = Completing the square

And actually, there are equation solvers out there that'll do this sort of thing, but I didn't want to make it that easy... :p

[edit: fixed a phrase-quote]

Last edited by AySz88 on Thu Mar 29, 2007 5:31 am, edited 2 times in total.

[Jerch]

...

And actually, there are equation solvers out there that'll do this sort of thing, but I didn't want to make it that easy... :p

That's what I've done..... I simply entered the two equations onto a graphing calculator, found the intersection, and carried out the necessary calculations.

[Siouxper]

Dear Zach,

Congratulations! You have guessed correctly in the Lenny Conundrum game (round 208). You have won 275 NP!

Yours Sincerely,
The Neopets Team!

Yay! Second week in a row!

(Too bad I didn't get much)

[TDG]

The working

Let Y be the larger of the two numbers
Let X be the smaller of the two numbers

Y - X = 12
Y * X = 17

X = Y-12

Y * (Y-12) = 17 (Substituting X=(Y-12) into second equation)

(Y^2) - 12Y - 17 = 0

Using the quadratic formula

Y = 13.28010989 or Y = -1.280109889

Assume that you cannot have a negative answer as the two results possible for X (which can be worked separately) are both positive and Y > X

X = Y - 12
X = 13.28010989 - 12
X = 1.28010989

(Y*100) + (X*50) = Z

Z = 1328.010989 + 64.0054945
Z = 1392.016484
Z = 1392 Neopoints (what a bargain!)