Summer+Math+Homework

This is my IGCSE Paper 6 Investigation.

7x+11y=100

This are the first sets of numbers.



- In the column on the left we have numbers 1 to 10 and in the column on the right we have the number that added to the number on the left will add up to 100.

-The first number -or the number on the column on the left- should be a multiple of 7, and the second number or the number in the column on the right should be a muliple of 11.

-The only multiple of 7 on the column on the left is 7 and the only multiple of 11 on the column on the right is 99 and they are not on the same row so that is not a posible answer.

I will try to do it with only multiples of 7 on the column on the left. Then I will write a number in the column on the right that adding it to the number in the left will give me 100.

-you can notice that the multiple of 7 is adding seven as it goes down and the other number is substracting seven as it goes down.

In my second set of numbers you can see that I have got an answer.

56 and 44

let's check if it is correct.

56/7=8 44/11=4

so x=8 and y=4

7(8)+11(4)=100

56+44=100

my first answer:

x1=8 and y1=4

is correct!

Lets keep on writing multiples of 7 to se if we can find something else.



-no, there are no more ansers undiscovered in the positive numbers.

Now lets see if we find something in the negatives.

On the column on the left have the multiples of seven (again) in negative, this number should be smaller than 100 if we are adding it with a positive. On the column on the right there will be a number that added to the multiple of 7 will give me 100, this number will be a positive.



I this set of numbers I found 4 results.

-21 and 121 -98 and 198 -175 and 275 -252 and 352

Lets check them:

i will start with: -21 and 121

-21/7=-3 so x=-3

121/11=11 so y=11

x=-3 y=11

7(-3)+11(11)=100

-21+121=100

My answer:

x=-3 y=11

is correct!

-98 and 198

-98/7=-14 so x=-14

198/11=18 so y=18

x=-14 y=18

7(-14)+11(18)=100

-98+198=100

My answer:

x=-14 y=18

is correct!

-175 and 275

-175/7=-25 so x=-25

275/11=25 so y=25

7(-25)+11(25)=100

-175+275=100

My answer:

x=-25 y=25

is correct!

-252 and 352

-252/7=-36 so x=-36

352/11=32 so y=32

7(-36)+11(32)=100

-252+352=100

My answer:

x=-36 y=32

is correct!

This are my values of x and y:



You can notice that value of x is substracting 11 each time, and the values of y are adding 7 each time.

you can find the next values of x using this equation:

Xn=8-11(n-1)

and you can find the next value of y using this equation:

yn=4+7(n-1)

lets check if my equation is correct using one of the values I found in the first part of the investigation.

lets use x3 and y3

lets start with x:

X3=8-11(3-1)

X3=8-11(2)

X3=8-22

X3=-14

now lets continue with y:

y3=4+7(3-1)

y3=4+7(2)

y3=4+14

y3=18

X3=-14 y3=18

7(-14)+11(18)=100

-98+198=100

it worked for this values but lets try again.

this time for X5 and y5

lets start with X5

X5=8-11(5-1)

X5=8-11(4)

X5=8-44

X5=-36

lets continue with y5

y5=4+7(5-1)

y5=4+7(4)

y5=4+28

y5=32

X5=-36 y5=32

7(-36)+11(32)=100

-252+352=100

it worked for this values but now lets try with values that are not in my investigation list.

X20 and y20

lets start with X20

X20=8-11(20-1)

X20=8-11(19)

X20=8-209

X20=-201

now with y20

y20=4+7(20-1)

y20=4+7(19)

y20=4+133

y20=137

X20=-201 y20=137

7(-201)+11(137)=100

-1407+1507=100

so it works for this as well so my equation does work.