Answer:
Step-by-step explanation:
Part a
We need two inequalities, one for time worked at each job and the other 
for amounts of money earned.
time:  Let b and c represent the time (number of hours) worked at babysitting and landscaping respectively.  Then b + c ≤ 20 hrs/wk
earnings:  Let ($3/hr)(b) represents the amount of money earned babysitting for b hour.  Let  ($7/hr)(c) represent the money earned working at landscaping.  These amounts are <em>per week</em>.  The appropriate inequality is  ($3/hr)(b) +  ($7/hr)(c) ≥ $84 per week.  The other inequality is 
b + c ≤ 20 hrs/wk.
Part b:
As before, b + c ≤ 20 hrs/wk.  What happens if Chet spends all his 20 hours babysitting?  To answer this, set c = 0 (no landscaping hours).  Then b ≤ 20 hours.  At $3/hr, he could earn only $60 and have no time left for landscaping.  Not good.
Let's experiment:  suppose he works 15 hours babysitting and 5 hours landscaping.  His earnings would be $45 + $35, or $80.  Still not enough; he wants to earn $84 total.    Let's redistribute his time and try again:  suppose he works 14 hours babysitting and 6 hours landscaping; his earnings would be $42 + $42, or $84.  So {b = 14 hours and c + 6 hours} is a solution.  As we continue to reduce the number of hours Chet works babysitting and correspondingly increase those he works landscaping, his earnings will go up, beyond $84.
Here's a table that summarizes this:
babysitting          landscaping    total amount
   hours                   hours               earned
       15                          5                      $60 (not acceptable)
        14                         6                       $84 (borderline acceptable)
        12                          8                       $36 + $42 = $78 (great)
         6                          14                       $116 (greater still)
          2                          18                     $132
           1                           19                      $134
           0                          20                      $140
Summary:  Chet can work anywhere from 0 to 14 hours babysitting and expect to earn $84 or more.