Questions: The sum of three numbers is 159 . The second number is 5 more than the first number, and the third number is 9 times the first number. Find the second number. (A) 82 (B) 19 C 126 D 28

Solution Steps

Let the first number be \( x \). According to the problem, the second number is 5 more than the first number, so we can express it as \( x + 5 \). The third number is 9 times the first number, which can be expressed as \( 9x \).

The sum of the three numbers is given as 159. Therefore, we can set up the equation:

\[ x + (x + 5) + 9x = 159 \]

Combine like terms in the equation:

\[ x + x + 5 + 9x = 159 \]

\[ 11x + 5 = 159 \]

Subtract 5 from both sides of the equation:

\[ 11x = 154 \]

Divide both sides by 11 to solve for \( x \):

\[ x = \frac{154}{11} = 14 \]

The second number is \( x + 5 \). Substitute \( x = 14 \) into this expression:

\[ x + 5 = 14 + 5 = 19 \]

Final Answer