Question

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

a. what is the minimum amount you can earn in a week?
b. write and solve an inequality that represents the numbers of cell phones you must sell to make at least $630 a week.
c. write and solve an inequality that represents the numbers 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 numbers of cell phones you can sell each week.

Explanation:

Step1: Analyze part a

Let \(x\) be the number of cell - phones sold. The weekly salary is composed of a base salary of \(150\) and \(20\) per phone sold. The total weekly earnings \(y = 150+20x\). To find the minimum amount earned in a week, we assume \(x = 0\). So \(y=150\).

Step2: Analyze part b

The inequality for earning at least \(630\) is \(150 + 20x\geq630\).
Subtract \(150\) from both sides: \(20x\geq630 - 150\).
\(20x\geq480\).
Divide both sides by \(20\): \(x\geq\frac{480}{20}=24\).

Step3: Analyze part c

The inequality for earning at least \(750\) is \(150+20x\geq750\).
Subtract \(150\) from both sides: \(20x\geq750 - 150\).
\(20x\geq600\).
Divide both sides by \(20\): \(x\geq\frac{600}{20}=30\).

Step4: Analyze part d

The inequality for earning at most \(950\) is \(150 + 20x\leq950\).
Subtract \(150\) from both sides: \(20x\leq950 - 150\).
\(20x\leq800\).
Divide both sides by \(20\): \(x\leq\frac{800}{20}=40\).

Answer:

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