Discussion
A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?
Answer: B
The number is 72.
Write the number as 10a + b. Subtracting 45 reverses the digits:
\[ \begin{aligned} 10a + b - 45 &= 10b + a \\ 9(a - b) &= 45, \ a - b = 5 \\ a + b &= 9 \Rightarrow a = 7,\ b = 2 \end{aligned} \]
Check: 72 - 45 = 27. The other options fail: 63 - 45 = 18, 81 - 45 = 36 and 90 - 45 = 45, none of which reverses the digits.
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