The product of the digits of a two-digit numb | vedclass

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(D) Let the tens digit be $x$ and the units digit be $y$. The number is $10x + y$.Given that the product of the digits is $14$,so $xy = 14$.When the d

Vedclass · Accepted Answer

$27$

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(D) Let the tens digit be $x$ and the units digit be $y$. The number is $10x + y$.Given that the product of the digits is $14$,so $xy = 14$.When the digits are interchanged,the new number is $10y + x$.According to the problem,the new number is $45$ more than the original number:$(10y + x) - (10x + y) = 45$$9y - 9x = 45$$y - x = 5$,which implies $y = x + 5$.Substitute $y = x + 5$ into $xy = 14$:$x(x + 5) = 14$$x^2 + 5x - 14 = 0$$(x + 7)(x - 2) = 0$Since $x$ must be a positive digit,$x = 2$.Then $y = 2 + 5 = 7$.The original number is $10(2) + 7 = 27$.

The product of the digits of a two-digit number is $14$. The number obtained by interchanging the digits is $45$ more than the original number. Find the original number.

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