You worked 14 hours last week and earned a total of $96 before taxes. Your job as a lifeguard pays $8 per hour, and your job as a cashier pays $6 per hour. How many hours did you work at each job?

The goal in these types problems is usually to solve two equations with two unknowns. The hard part for most people is deciphering from the words what those two equations are. In this case, for example, the question is asking for the number of hours you worked at each job, so those are your two unknowns (you could call them "a" and "b" when you write your equations). So now you need to look at all the information you're given and write down the equations. The first part, for example, says you worked 14 hours last week, so you know right away that the sum of the two unknowns must be 14. That's one equation right there! For the second equation, you know that the total money you earned from both jobs was $96. Can you figure out that equation now?

Once you have your two equations, you simply solve one of them for one of the variables and then substitute the result into the other equation.

I'll give you an example of substitution (though not with the same equations as this problem asks; you'll need to figure those out for yourself):

Let's say we have these two equations:

a + b = 10
3a - 4b = 9

We can solve the first equation for a:

a = 10 - b

Now, we take that solution and plug it in everywhere we see an "a" in the second equation:

3(10 - b) - 4b = 9

Now it's just a matter of solving for b:

b = 3

Finally, to get a, we just plug our value for b back into either one of the equations:

a + 3 = 10, so
a = 7

That's it! You just need to do the same thing for your two equations.

Finally, when you're all done, just check your work to make sure it passes the common sense test. Do the total hours add up to 14? Does the total money earned work out to be $96? If so, good job!

If the sum of two numbers is 13 and the difference is 5, what are the numbers?