calculating time and half algebra question

Question

pretty basic, but my mind is spinning from all the algebra I am reviewing. Here is the question: 

 

Person is paid time and a half for every hours they work past 36 hours in a week. Last week the person worked 42 hours and made $472.50. What is their normal rate of pay?

 

Ok, how do I set this up? 

Answer 1

Here's how you do it:

 

The person gets paid two different salaries: one for the first 36 hours, and another for the remaining 6 hours (42 - 36 = 6).

 

We can call these salaries x and y.  Now we have an equation:

 

36x + 6y = 472.50

 

But we need to get this equation down to only one variable.  Well, we also know that y = 1.5x (because the latter 6 hours, the person is paid 1.5x times the original salary).  Using substitution, you get:

 

36x + 6(1.5x) = 472.50

45x = 472.50

x = $10.50/hour