For a remodeling project, a contractor charges a certain hourly rate

• Rate of skilled Labor = \(\frac{$S }{ \text{hour}}\)
  
• Rate of unskilled Labor = \(\frac{$U }{ \text{hour}}\)

Given: \(U < S\)

Question: \(50S + 70U =\) ?

Statement 1

(1) The hourly rate charged by the contractor for unskilled labor is 30 percent less than the hourly rate charged by the contractor for skilled labor.

U = 0.7S

However, as we do not know the value of S, we can't find the total value i.e. the value of 50S + 70U. Hence, the statement alone is not sufficient.

Eliminate A and D.

Statement 2

(2) The hourly rate charged by the contractor for unskilled labor is $18 less than the hourly rate charged by the contractor for skilled labor.

S - U = 18

However, as we do not know the value of S, we can't find the total value i.e. the value of 50S + 70U. Hence, the statement alone is not sufficient.

Eliminate B.

Combined

From Statement 1, we know that the hourly rate charged by the contractor for unskilled labor is 30 percent less than the hourly rate charged by the contractor for skilled labor. From statement 2, we know the difference between the hourly rate charged by the contractor for unskilled labor and the hourly rate charged by the contractor for skilled labor is $18.

Hence, 30% of the hourly rate of the skilled labor = $18

\(0.3 S = 18\)

\(S = 60\)

The statements combined help us obtain the value of \(S\). Using the information of either Statement we can find the value of U. As the values of S and U can be obtained, we can also find the value of \(50S + 70U\).

The statements combined help.

Option C