The sum of the digits of a two-digit number i | vedclass

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(D) Let the digits of the two-digit number be $x$ and $y$.Given that the sum of the digits is $x + y = 15$ $(1)$.Given that the difference between the

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Cannot be determined

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(D) Let the digits of the two-digit number be $x$ and $y$.Given that the sum of the digits is $x + y = 15$ $(1)$.Given that the difference between the digits is $x - y = 3$ $(2)$ or $y - x = 3$ $(3)$.Case $1$: Solving $(1)$ and $(2)$:Adding the equations,$2x = 18 \Rightarrow x = 9$.Substituting $x = 9$ into $(1)$,$9 + y = 15 \Rightarrow y = 6$.Thus,the number is $96$.Case $2$: Solving $(1)$ and $(3)$:Adding the equations,$2y = 18 \Rightarrow y = 9$.Substituting $y = 9$ into $(1)$,$x + 9 = 15 \Rightarrow x = 6$.Thus,the number is $69$.Since both $96$ and $69$ satisfy the given conditions,the specific two-digit number cannot be uniquely determined.Therefore,the correct option is $(d)$.

The sum of the digits of a two-digit number is $15$ and the difference between the digits is $3$. What is the two-digit number?

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