Question

1. this question has two parts. first, answer part a. then, answer part b. part a bakery aisha can work up to 20 hours per week. working at a bakery, she earns $7 per hour most of the time and $8.50 per hour during the early morning shift. aisha needs to earn at least $150 this week to pay for a trip with her friends. determine the number of regular and early morning hours that aisha could work. part a select the correct system and graph. let r = regular hours and m = early morning hours. o a) r < 20 7r + 8.5m ≥ 150 o b) r + m ≤ 20 r + m ≤ 150 o c) r + m ≤ 20 7r + 8.5m ≥ 150 o d) 7r + 8.5m > 20 7r + 8.5m ≥ 150 part b circle every viable solution. (2,17) (4,7) (5,15) (8,13) (10,10) (18,6) (21,6)

Explanation:

Step1: Analyze the constraints

Aisha can work up to 20 hours per week, so $r + m\leq20$. She needs to earn at least $150$, so $7r + 8.5m\geq150$.

Step2: Check Part A options

Option A has $r<20$ instead of $r + m\leq20$, Option B has $r + m\leq150$ which is wrong earnings - related constraint, Option D has $7r + 8.5m>20$ which is wrong inequality for earnings. Option C has $r + m\leq20$ and $7r + 8.5m\geq150$ which is correct.

Step3: Check Part B solutions

For $(r,m)$ pairs:

• For $(2,17)$: $r + m=2 + 17=19\leq20$ and $7r + 8.5m=7\times2+8.5\times17 = 14 + 144.5=158.5\geq150$.
• For $(4,7)$: $r + m=4 + 7 = 11\leq20$ and $7r + 8.5m=7\times4+8.5\times7=28 + 59.5 = 87.5<150$ (not valid).
• For $(5,15)$: $r + m=5 + 15=20\leq20$ and $7r + 8.5m=7\times5+8.5\times15=35 + 127.5 = 162.5\geq150$.
• For $(8,13)$: $r + m=8 + 13=21>20$ (not valid).
• For $(10,10)$: $r + m=10 + 10=20\leq20$ and $7r + 8.5m=7\times10+8.5\times10=70 + 85 = 155\geq150$.
• For $(18,6)$: $r + m=18+6 = 24>20$ (not valid).
• For $(21,6)$: $r + m=21 + 6=27>20$ (not valid).

Answer:

Part A: C. $r + m\leq20$, $7r + 8.5m\geq150$
Part B: $(2,17)$, $(5,15)$, $(10,10)$