A two-digit number is 4 times the sum of its digits. If the digits are interchanged, the new number is 18 more than the original. Find the number.

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1. Let the tens digit be $x$ and the units digit be $y$. The number is $10x+y$.

2. Given $10x+y=4(x+y)$. Simplify: $10x+y=4x+4y\Rightarrow6x=3y\Rightarrow y=2x$.

3. When digits are interchanged, the number is $10y+x$. Given $10y+x=(10x+y)+18$. Substitute $y=2x$: $10(2x)+x=10x+2x+18\Rightarrow21x=12x+18\Rightarrow9x=18\Rightarrow x=2$, so $y=4$.

4. The original number is $10x+y=10\cdot2+4=24$. **Answer: 24**

FINAL_ANSWER: b

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