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Mathematics

The sum of two numbers is 53 and their difference is 25. Find the numbers.

Linear Equations

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Answer

Let two whole numbers be x and y, where x > y.

Given,

Sum of numbers = 53

⇒ x + y = 53     …….(1)

Difference of numbers = 25

⇒ x - y = 25     ……(2)

Adding equations (1) and (2), we get :

⇒ (x + y) + (x - y) = 53 + 25

⇒ x + x + y - y = 78

⇒ 2x = 78

⇒ x = 782\dfrac{78}{2} = 39.

Substituting value of x in equation (1), we get :

⇒ x + y = 53

⇒ 39 + y = 53

⇒ y = 53 - 39 = 14.

Hence, the numbers are 39 and 14.

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