Plz ! 10

chet has at most 20 hours a week available to work during the summer, dividing that time between making $3 an hour babysitting and $7 an hour working for a landscaping company. chet needs to accumulate at least $84 per week.

(a) write a system of inequalities that describes the given conditions.

(b) what are all the possible hours chet can work babysitting and still earn at least $84?

s much! i can't you enough!

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 per week.  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.

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step-by-step explanation: