Question

Find 2 numbers, if their sum is -11 and their difference is 41

Answer 1

15, -26

Explanation:

The generic solution to a "sum and difference" problem can be found easily. Let "a" and "b" represent the numbers you seek, and let "s" and "d" represent their sum and difference:

a + b = s

a - b = d

Adding these two equations tells you ...

2a = s + d

a = (s + d)/2 . . . . . . divide by the coefficient of a

You can find "b" several different ways. One way is to subtract the second equation from the first:

2b = s - d

b = (s - d)/2 . . . . . . divide by the coefficient of b

So, the second number can be found from any of ...

b = s - a

b = a - d

b = (s - d)/2

____

For the numbers given here, s=-11, d=41, the two numbers are ...

a = (-11 +41)/2 = 15

b = -11 -15 = -26

The two numbers are 15 and -26.

Answer 2

15, -26

Explanation:

The generic solution to a "sum and difference" problem can be found easily. Let "a" and "b" represent the numbers you seek, and let "s" and "d" represent their sum and difference:

a + b = s

a - b = d

Adding these two equations tells you ...

2a = s + d

a = (s + d)/2 . . . . . . divide by the coefficient of a

You can find "b" several different ways. One way is to subtract the second equation from the first:

2b = s - d

b = (s - d)/2 . . . . . . divide by the coefficient of b

So, the second number can be found from any of ...

• b = s - a
• b = a - d
• b = (s - d)/2

____

For the numbers given here, s=-11, d=41, the two numbers are ...

a = (-11 +41)/2 = 15

b = -11 -15 = -26

The two numbers are 15 and -26.