word problem4

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number is equal to 3 less than four times the original number. What is the original number?

let digit in unit's place be x and that in ten's place of the original number be y

original number = 10y + x

given
x + y = 7 ----------(i) (sum of digits)

after the digits are reversed, the new number is 10x + y

given that new number = 4*(original number ) -3
therefore ( 10 x +y) = 4*(10y + x ) - 3

or 10x + y = 40y + 4x - 3
or 6x -39 y = -3 ----------(ii)

system is
x + y = 7 ----------(i)
6x - 39 y = -3 ----------(ii)

solving
eliminating x
6x + 6y = 42----------(i)
6x - 39 y = -3 ----------(ii)

subtracting
45 y = 45 or y =1
substituting x + 1 = 7 or x = 6

therefore
x = 6 , y = 1

original number = 16

other word problems with some explanation


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