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

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In this Question the difference between the numbers and their square is given.
You have to find the numbers.
This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.
This is the Question Number 10 Of Exercise 3E of RS Aggarwal Solution.

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1 Answer

  1. 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

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