The difference of two numbers is 2. Their sum is 8. What are the numbers ?

Answer 1

If the numbers are x and y then you will have 2 equations. When x<y:

y - x = 2 y + x = 8

Solve for possible answers using each equation:

Difference Sum

y - x = 2 y + x = 8

10 - 8 = 2 7 + 1 = 8

9 - 7 = 2 6 + 2 = 8

8 - 6 = 2 5 + 3 = 8

7 - 5 = 2 4 + 4 = 8

6 - 4 = 2

5 - 3 = 2

4 - 2 = 2

Make x and y pairs:

Difference Sum

10 and 8 7 and 1

9 and 7 6 and 2

8 and 6 5 and 3

7 and 5 4 and 4

6 and 4

5 and 3

4 and 2

Finally find a pair that fits in both equations:

5 and 3 are the numbers

Summary

5 and 3 fit as the required pair because (5 - 3) = 2 and (5 + 3) =8. This pair fits the difference of 2 and sum of 8 requirements. 5 and 3 were found using the equations (y>x) y - x = 2 and y + x = 8

Answer 2

Let the numbers be x and y where x > y:

x - y = 2

x + y = 8 => add the two equations:

2x = 10

x = 5

y = 3