Explanation

This question gives us pretty standard word problem material. Expressing what we are being told in mathematical terms, we are looking for the value of , the cost of the 10 hours. We might get it by learning the values of a and b, or we might get it through fortuitous algebra that yields the phrase directly. Let's go to the data statements, looking at them separately first.

Statement (1): two hours means one hour at the rate a and one hour at the rate b, so the statement is telling us that . This is only one equation for two variables, so we can't solve completely. Moreover, we can't massage it into in any way that doesn't put variables on the other side of the equation. Insufficient.

Statement (2): by similar logic, we are told . And for the same reasons as above, this statement is insufficient. Note that we can't just double the cost to get the cost of 10 hours, because it's not a flat rate and we don't know the cost of the first hour, a.

Combining, we'll be able to solve. We have two distinct equations to use to solve for the two variables. The methods of solving are covered in the Math Review of this course and also in Problem Solving questions. The easiest way to see that the equations are distinct is that they have a similar form and one is not a multiple of the other.

The correct answer is (C).