Question

Both of these questions have to deal with using inverses to linear systems:
1. Work Schedule You worked 18 hours last week and earned a total of $124 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?
2. Law Enforcement During one calendar year, a state trooper issed a total of 385 citations for warning and speeding tickets. Of these, there were 31 more warnings than speeding tickets. How many warnings and how many speeding tickets were issued?

Answer 1

For the first question, I think you need to set up the equation first.
Let x be the number of hours you worked as a lifeguard, then the number of hours you worked as a cashier is ...??

Answer 2

Hint: (For the first one)

x = life guard hours
y = cashier hours

x + y = 18
8x + 6y = 124(18)

I don't get what they mean by "inverses" to linear systems

Answer 3

@Callisto, do you have a clue what they mean by that?

Answer 4

Actually, I have no ideas about that. But we can solve the problems by setting up equation.

Btw, since the total working hour is 18, when we let x be the working hours as the lifeguard, working hours as a cashier can be found be subtracting x from 18. In this way, we just need one equation.

Answer 5

I already know that. I just prefer setting up a system of equations. The reason is so that if I ever need to, I can always just graph both equations and check the values that way.

Answer 6

I just wanted to know what they meant by "inverse" linear system

Answer 7

Got it!