Question

Parker is working two summer jobs, making $11 per hour lifeguarding and $22 per hour tutoring. Last week Parker worked a total of 16 hours and earned a total of $242. Determine the number of hours Parker worked lifeguarding last week and the number of hours he worked tutoring last week.

Answer 1

Answer:

10 hours lifeguarding, 6 hours tutoring

Step-by-step explanation:

As you know how long he worked and how much he earned, it's worth seeing how many hours it would have been had he worked just tutoring or just lifeguarding.

$242 / 11 = 22 hours if it was just lifeguarding

$242 / 22 = 11 hours (as it's exactly double the wage) if it was just tutoring

We now know that he worked some combination of both

Calculating his average wage can help work out which he worked more of:

$242 / 16 = 15.125

That means Parker's average hourly wage was 15.125 which is closer to 11 than 22 (16.50 would mean an exactly even split between the two) so he did more hours lifeguarding than tutoring so more than 8 hours.

What I then do is consider the variations that could work:

9 (lifeguarding) and 7 (tutoring) = 99 + 154 = 243

So we're almost exactly there straight away, but not quite so...

10 and 6 = 110 + 132 = 242

There you have it.

Answer 2

We can use the equations: 11x + 22y= 242 and x+y=16 to solve in a system of equations to determine the number of hours that Parker worked for each job.

Our system of equations would be
(I’m using the elimination method)
11x + 22y= 242
x+y=16
+______________
And I will multiply the top equation by - 1/11 to get easier numbers to work with.

So we get:
-x-2y=-22
x+y=16
+_______

And solving it we get:
-y=-6
y=6

And we plug in y=6 into one of the equations to get x.

x+6=16
x=10.

So Parker works 10 hours lifeguarding and 6 hours tutoring last week.

*** I used x as lifeguarding and y as the tutoring hours.

I hope this helps!