What are the two numbers that the sum is 19 and the difference is 1?

Answer 1

You can work this out by expressing the two given facts and substituting one into the other. We'll call the numbers "a" and "b". We're told:

The sum (of the two numbers) is 19, or "a + b = 19"

The difference (between them) is 1, or "|a - b| = 1"

First, let's rearrange the first one, solving for a:

• a + b = 19
• a = 19 - b

now we can take that definition of a, and plug it in to the second equation:

• |a - b| = 1
• |(19 - b) - b| = 1
• |19 - 2b| = 1
• 19 - 2b = ± 1
• -2b = -19 ± 1
• 2b = 19 ± 1
• 2b = 18, 20
• b = 9, 10

So b = either 9 or 10, now plug that into one of the originals to solve for a:

• a + b = 19
• case 1:
• a + 9 = 19
• a = 10
• case 2:
• a + 10 = 19
• a = 9

and there's your answer, either:

a = 9 and b = 10

or:

a = 10 and b = 9

Answer 2

14 AND 5

Answer 3

s

Answer 4

12,5