math+project

Investigation 7x+11y

First I examine for all the integers positive and the negatives.

11+89=100 22+78=100 33+67=100 44+56=100 55+45=100 66+34=100 77+23=100 88+12=100 99+1=100

there was only one positive integers, the negatives are:

-11+111=100 -22+122=100 -33+133=100 -44+144=100 -55+155=100 -66+166=100 -77+177=100 -88+188=100 -99+199=100 -110+210=100 - 121+221=100   -132+232=100  -143+243=100  -154+254=100  -165+265=100  -176+276=100  -187+287=100

I already find 3 negative integers and to find i put the table of eleven in negative numbers and then i finded all de values for them.


 * VALUES **

44+56=100 Y=4 X=8

-33+133=100 Y=-3 X=14

-110+210=100 Y=-10 X=30

-187+287=100 Y=-17 X=41

FORMULA

X=8+11(N-1) Y=4-7(N-1)

I finded this rule beacuase a noticed a pattern and X positive the difference the numbers in the equiation.

TESTING THE FORMULAE

8+11(6-1) 4-7(6-1)

X=63 Y=31

7(63)+11(-31)=100 441+-341=100

I tested this formulae many times to show that is correct.