What is high powered geometry?

Main Question or Discussion Point

When ever my teacher comes to a very complicated problem he says there is a way to solve it using highpowered geometry. But never showed an example or really talked about it much.

Solving such advanced problems with highpowered geometry sounds interesting. Can anyone please enlighten me on this, and give an example of it at work?

Integral
Staff Emeritus
Gold Member
It would help if you posted a specific example along with the method of solution used by your teacher. Perhaps then we could show a different method.

He never showed any solution that he said "to solve the method is too complex for you to understand" some similar like that. Heres an example recently

Penniless Pete's piggy bank has no pennies in it, but it has 100 coins all nickels, dimes, and quarters, who's total value is \$8.35. It does not necessarily contain coins of all three types. What is the difference between the largest and smallest number of dimes that could be in the bank?

Getting maximum is easy, just don't use quarters and you get
Code:
a =amount of dimes
b = amount of nickels
a(10)+b(5)=835 (cents)
a + b =100 <-- multiply this by 5 and "solve by collumbs"
to get rid of "b", and we get maximum

a(10)+b(5)=835
5a + 5b = 500
-----------------
5a = 335
a = 335/5
a = 67

Minimum seems impossible. This question is multiple choice
(A)0 (B)13 (C)37 (D)64 (E)83
if 67 is maximum dimes than one of
those must be subtracted to get minimum lets test each

67-64 = 3
c = quarters
3(10) + 5b + 25c = 835
5b + 25c = 805
b + c + 3 = 100

b+c=97

5b + 5c=485
5b + 25c = 805
-------------------
20c = 320
c=16
I got 16 which is a whole number, thus it is agreeable. So lets say I didn't have the multiple choices, how would I solve it?

Last edited:
mathwonk