A two-digit number is 4 times the sum of its digits. If the digits are reversed, the new number is 18 more than the original. What is the number?
24
Let the number be 10a + b, where a is the tens digit and b is the units digit.
Condition 1: Number = 4 × (sum of digits)
\(10a + b = 4(a + b) \implies 10a + b = 4a + 4b \implies 6a = 3b \implies b = 2a\)
Condition 2: Reversed number is 18 more than original.
\((10b + a) - (10a + b) = 18 \implies 9b - 9a = 18 \implies b - a = 2\)
From the two equations: 2a − a = 2 ⇒ a = 2, so b = 4.
Number = 10(2) + 4 = 24.
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