Math(investigation+paper+6)

IGCSE investigation

Try one (positive 7 and positive 11)

multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77. multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121

56 + 44= 100

try two (negative 7 + positive 11) multiples of -7: -7,-14, -21 ,-28,-35,-42,-49,-56,-63,-70,-77,-84,-91, -98 ,-105,-112,-119,-126,-133,-140,-147,-154,-161,-168, -175, -182,-189,-196,-203,-210,-217,-224,-231,-238,-245, -252 ,-259,-266,-273,-280,-287,-294,-301,-308,-315,-322, -329 ,-336,-343,-350,-357,-364,-371,-378,-385,-392,-399, -406 ,-413,-420,-427,-434,-441,-448,-455,-462,-469,-476, -483 ,-490,-497,-504,-511,-518,-525,-532,-539,-546,-553, -560, -567,-574, -581

multiples of 11:

11,22,33,44,55,66,77,88,99,110, 121 ,132,143,154,165,176,187, 198 ,209,220,231,242,253,264 ,275 ,286,297,308,319,330,341, 352 ,363,374,385,396,407,418, 429 ,440,451,462,473,484,495, 506 ,517,528,539,550,561,572, 583 ,594,605,616,627,638,649 ,660 ,671

-21 + 121= 100 -98 + 198= 100  -175 + 275= 100  -252 + 352= 100  -329 + 429= 100  -406 + 506= 100  -483 + 583= 100  -560 + 660= 100

try three multiples of 7: 7 ,14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168 175 182 189 196 203 210 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287 , 294,301, 308,315,322,329,336,343,350,357, 364 ,371,378,385,392,399,406,413,420,427,434, 441, 448,455,462,469,476,483,490,497,504,511, 518 ,525,532,539,546,553,560,567,574,581,588, 595 ,602,609,616,623,630,637,644,651,658,665, 672 ,679

multiples of 11:

-11,-22, -33 ,-44,-55,-66,-77,-88,-99, -110 ,- 121 ,-132,-143,-154,-165,-176, -187 ,- 198 ,-209,-220,-231,-242,-253 ,-264 ,-275 ,-286,-297,-308,-319,-330, -341 ,- 352 ,-363,-374,-385,-396,-407, -418, -429 ,-440,-451,-462,-473,-484, -495 ,- 506 ,-517,-528,-539,-550,-561, -572 ,- 583 ,-594,-605,-616,-627,-638,-649 , -660 ,-671

-33 + 133= 100 -110 + 210= 100 -187 + 287= 100 -264 + 364= 100 -341 + 441= 100 -418 + 518= 100 -495 + 595= 100 -572 + 672= 100

Do you notice a pattern? yes, in the first chart the pattern is -11. And i the two charts the patterns is of +7

Can you make equations that describes how you get from one value of x and y to the next value?

The only equiations that works with two possitive integers is: x=56( 7 x 8) y=44( 11 x 4) = 56 + 44 =100

this only works with positive integers because the other are with one negative integers.

example:

X= 133( 19 x 7) Y= -33( -33 x 11) 133-33 100 X= -98( -14 x 7) Y=198( 188 x 11) 198-98 100

formula: x= 8-11 i found this equation when i notice that the difference between each integers was -11 y= 4 + 7 i found this equations when i notice the difference of each integers was +7

N=8

x=8-11(8-1) =8-1=7 =7 x -11=-77 =8-77=-69 -69 x 7= -483

Y= 4 + 7 (8-1) =8-1=7 =7 x 7=49 =49 + 4=53 53 x 11= 583

Y+X= 583-483= 100