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

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(B) 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 $xy = 15$.When the digits ar

Vedclass · Accepted Answer

$35$

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(B) 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 $xy = 15$.When the digits are interchanged,the new number is $10y + x$.According to the problem,the new number is $18$ more than the original number:$(10y + x) - (10x + y) = 18$$9y - 9x = 18$$y - x = 2$,which implies $y = x + 2$.Substitute $y = x + 2$ into the product equation $xy = 15$:$x(x + 2) = 15$$x^2 + 2x - 15 = 0$$(x + 5)(x - 3) = 0$Since $x$ must be a positive digit,$x = 3$.Then $y = 3 + 2 = 5$.The original number is $10(3) + 5 = 35$.

The product of the digits of a two-digit number is $15$. If the digits of this number are interchanged,the new number so obtained is $18$ more than the original number. Find the original number.

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