Question

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

Answer 1

Hi ,

Convert this word problem into

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

x^2 - y^2 = 448

( x + y ) ( x - y ) = 448

( x + y ) × 14 = 448

[ from ( 1 ) ]

x + y = 448/ 14

x + y = 32 ----( 2 )

Add equations ( 1 ) and ( 2 ) , we get

2x = 46

x = 46/2

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

I hope this helps you.

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Answer 2

check the answer first