Question

The sum of two mumbers is 21 and their difference is 7. What are the numbers?

Answer 1

`\text{Method 1:}\\\text{Let the two numbers be }x\text{ and }y.\\\text{First condition:}\\x+y=21...(1)\\x-y=7...(2)\\\text{Adding equations(1) and (2),}\\2x=28\\\text{or, }x=14\\\text{Equation(2) becomes}\\14-y=7\\\text{or, }y=7\\\text{So the two numbers are 14 and 7.}`

`\text{Method 2:}\\\text{Let the two numbers be }x\text{ and }21-x.\\\text{Let the greater number be }21-x.\\\text{Since the difference between these numbers is 7,}\\21-x-x=7\\\text{or, }21-2x=7\\\text{or, }2x=14\\\text{or, }x=7\\\therefore \text{The other number = }21-x=21-7=14.`

`\text{Method 3:}\\\text{Let the two numbers be }x\text{ and }x+7.\\\text{Since the sum of these numbers is 21,}\\x+x+7=21\\\text{or, }2x+7=21\\\text{or, }2x=14\\\text{or, }x=7\\\therefore\ \text{The other number = }x+7=7+7=14.`