1. sana works part - time in event management earning $20 per hour. she also does freelance carpentry…

1. sana works part - time in event management earning $20 per hour. she also does freelance carpentry projects for $25 per hour. she wants to earn more than $750 per week.\n a. write an inequality to represent the scenario.\n b. graph the inequality.\n c. identify one possible solution to the inequality. is it reasonable in this context? why or why not?\n d. sana covers her basic expenses with $750, but wants to save up for a vacation. how much extra would she earn if she worked 30 hours in event management and 15 hours in carpentry?\n e. if sana cant find any hours of carpentry work, at least how many hours would she need to work in event management to meet her basic needs?\n f. what is the fewest number of hours that sana could work and still earn more than $750? justify your response.

1. sana works part - time in event management earning $20 per hour. she also does freelance carpentry projects for $25 per hour. she wants to earn more than $750 per week.\n a. write an inequality to represent the scenario.\n b. graph the inequality.\n c. identify one possible solution to the inequality. is it reasonable in this context? why or why not?\n d. sana covers her basic expenses with $750, but wants to save up for a vacation. how much extra would she earn if she worked 30 hours in event management and 15 hours in carpentry?\n e. if sana cant find any hours of carpentry work, at least how many hours would she need to work in event management to meet her basic needs?\n f. what is the fewest number of hours that sana could work and still earn more than $750? justify your response.

Answer

Explanation:

Step1: Define variables

Let (x) be the number of hours in event management and (y) be the number of hours in carpentry.

Step2: Write the inequality

Earnings from event management is (20x) and from carpentry is (25y). She wants to earn more than (750), so the inequality is (20x + 25y>750).

Step3: For part d

Calculate earnings: (20\times30+25\times15 = 600 + 375=975). Extra amount (=975 - 750 = 225).

Step4: For part e

If (y = 0), then (20x\geq750) (since she needs to meet basic needs). (x=\frac{750}{20}=37.5). Since hours can't be in fraction for work, (x = 38) hours.

Step5: For part f

To minimize total hours ((H=x + y)), from (20x+25y>750), rewrite as (4x + 5y>150). We want to minimize (H). Let's use the fact that we want to make the coefficients of (x) and (y) as close as possible. If (x = 25) and (y = 10), then (20\times25+25\times10=500 + 250=750) (not more). If (x = 26) and (y = 10), (20\times26+25\times10=520+250 = 770>750). Total hours (H=26 + 10=36).

Answer:

a. (20x + 25y>750) d. She would earn an extra ($225) e. (38) hours f. (36) hours (by checking combinations of (x) and (y) values that satisfy (20x + 25y>750) and minimizing (x + y))