IGCSE

Task: Write 100 as the sum of two integers, one divisible by 7 and the other divisible by 11. Use your answer to find formulas giving all the solutions of the following equation where x and y are integers.
 * MATH INVESTIGATION**
 * A new problem**

y = 100 - 7x ÷ 11. positive "x" : 1, 2, 3,....., "8" replacing x = 8 y = 100 - 7(8) y = 4.
 * 1)** 11y = 100 - 7x

The value of "y" is 4. Test: 7(8) + 11(4) = 100 56 + 44 = 100 100 = 100
 * 2)** The value of "x" is 8.

__﻿__ //﻿I started testing positive values for "x" ; and when replacing 8 I obtained "y" = 4-// //This is the only pair of numbers where "x" and "y" are positive. After that, I continued trying// //and for "x" = 19 I obtained "y" = -3// a) Negative integers for "x" and positive integers for "y". y = 100 - 7x ÷ 11. negative "x" : -1, -2, -3,....
 * 3,4)**
 * 3,4)**
 * x || -3 || -14 || -25 || -36 ||
 * y || 11 || 18 || 25 || 32 ||

b) Positive integers for "x" and negative integers for "y". y = 100 - 7x ÷ 11. positive "x" : 9, 10, 11...., 19,..


 * x || 19 || 30 || 41 || 52 ||
 * y || -3 || -10 || -17 || -24 ||
 * 5)** There is a pattern in this numbers,as shown above.

6, 7) a) Negative "x" and positive "y" are obtained with this formula. n: 1, 2, 3,... test: f(1) = -11(1) + 8 = -3 f(2) = -11(2) + 8 = -14 f(3) = -11(3) + 8 = -25 ...
 * f(n) = 11n + 8 ||

b) Positive "x" and negative "y" are obtained in this formula. n: 1, 2, 3, ... f(1) = 11(1) + 8 = 19 f(2) = 11(2) + 8 = 30 f(3) = 11(3) + 8 = 41...
 * f(n) = 11m + 8 ||

//I started trying negative values for "x". Starting with -1, when I replaced x= -3, I obtained y = 11.// //I continued replacing x= -14; x= -25; x= -36. I observed that the difference between them is of "-11"﻿.// //And I got the formula F(n) = 11n + 8.// //Similarly, with the positive "x" I continued from x= 19; x=30; x= 41; x=52. Observing that the diference// //between this numbers is 11, I obtained the formula F(n) = 11n + 8.//

By: Olga M.Castaneda, 9E//﻿// __﻿__ __﻿__