Question

1. your weekly base salary is $150. you earn $20 for each phone you sell.

a. what is the minimum amount you can earn in a week?
b. write and solve an inequality that represents the number of cell phones you must sell to make at least $630 a week.
c. write and solve an inequality that represents the number of cell phones you must sell to make at least $750 a week.
d. the company policy is that as a part - time employee, the maximum you can earn each week is $950. write and solve an inequality that represents the number of cell phones you can sell each week.

Explanation:

Step1: Analyze part a

The minimum amount is the base salary since selling 0 phones gives the lowest - earning case.

Step2: Analyze part b

Let \(x\) be the number of phones sold. The total earnings \(E = 150+20x\). We want \(E\geq630\), so \(150 + 20x\geq630\).
Subtract 150 from both sides: \(20x\geq630 - 150\), \(20x\geq480\).
Divide both sides by 20: \(x\geq\frac{480}{20}\), \(x\geq24\).

Step3: Analyze part c

Let \(x\) be the number of phones sold. The total earnings \(E = 150+20x\). We want \(E\geq750\), so \(150 + 20x\geq750\).
Subtract 150 from both sides: \(20x\geq750 - 150\), \(20x\geq600\).
Divide both sides by 20: \(x\geq\frac{600}{20}\), \(x\geq30\).

Step4: Analyze part d

Let \(x\) be the number of phones sold. The total earnings \(E = 150+20x\). We want \(E\leq950\), so \(150 + 20x\leq950\).
Subtract 150 from both sides: \(20x\leq950 - 150\), \(20x\leq800\).
Divide both sides by 20: \(x\leq\frac{800}{20}\), \(x\leq40\).

Answer:

a. \(\$150\)
b. The inequality is \(150 + 20x\geq630\), and the solution is \(x\geq24\)
c. The inequality is \(150 + 20x\geq750\), and the solution is \(x\geq30\)
d. The inequality is \(150 + 20x\leq950\), and the solution is \(x\leq40\)