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.
, we have
