The difference between two numbers is 14 and the difference between their squares is 448

Answer

The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.

Let the larger number be x and the smaller number be y.Then, we have:x – y = 14 or x = 14 + y                 ……….(i)`x^2 – y^2 = 448`                 ………(ii)On substituting x = 14 + y in (ii) we get`(14 + y)^2 – y^2 = 448``⇒ 196 + y^2 + 28y – y^2 = 448`⇒ 196 + 28y = 448⇒ 28y = (448 – 196) = 252`⇒ y = 252/28 = 9`On substituting y = 9 in (i), we get:x = 14 + 9 = 23

Hence, the required numbers are 23 and 9.

Concept: Pair of Linear Equations in Two Variables

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The difference between two numbers is 14 and the difference between their squares is 448 . Find the numbers.

Solution

Convert this word problem into an algebraic equation. Let the two numbers be x and y Difference between two numbers is equal to 14 x - y = 14 -----( 1 ) Difference between their squares is equal to 448

= 448

( x + y ) ( x - y ) = 448 ( x + y ) × 14 = 448 [ from ( 1 ) ]

x + y = 44814

x + y = 32 ----( 2 ) Add equations ( 1 ) and ( 2), we get 2x = 46

x = 462 ​​​​​​​ ​​​​​​​

x = 23 Put x = 23 in equation ( 2 ) 23 + y = 32 y = 32 - 23 y = 9 Therefore, Required two numbers are x = 23 and y = 9

Mathematics

Secondary School Mathematics X

Standard X