Question

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

Answer 1

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 = $\frac{448}{14}$

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

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

2x = 46

x = $\frac{46}{2}$ ​​​​​​​ ​​​​​​​

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