Question

8.8ab.2 micro - lesson
writing inequalities and real - world problems in one variable
write an inequality to represent the given situation.
1 ross is considering the income of two job offers. company a is offering a yearly salary of $37,500 plus one - time signing bonus of $10,000. company b is offering a yearly salary of $40,000 with no signing bonus.
write an inequality to find x, the number of years ross would have to work so that the total income at company b is greater than the total income at company a.
variable
constant rate
information
inequality
use the inequality to fill in the missing information in each statement. you do not need to solve the inequality.
2 chandler compares the cost of two electricians,
35x + 100 < 27x + 200
a) electrician a charges $______ per hour plus a flat fee of $______.
b) electrician b charges $______ per hour plus a flat fee of $______.
c) what is x, the ______
electrician a would have to work in order for the total cost to be greater than/less than (circle) the total cost for electrician b?
i can write one - variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants.
i can write a corresponding real - world problem when given a one - variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants.

Explanation:

Step1: Analyze Company A's total income

Company A has a yearly salary of $37500$ and a one - time signing bonus of $10000$. So the total income after $x$ years is $37500x + 10000$.

Step2: Analyze Company B's total income

Company B has a yearly salary of $40000$, so the total income after $x$ years is $40000x$.

Step3: Write the inequality

We want the total income at Company B to be greater than the total income at Company A. So the inequality is $40000x>37500x + 10000$.

For the second part:

Step1: Analyze the cost formula for Electrician A

In the inequality $35x + 100<27x+200$, for Electrician A, the coefficient of $x$ is the hourly rate and the constant is the flat - fee. So Electrician A charges $\$35$ per hour plus a flat fee of $\$100$.

Step2: Analyze the cost formula for Electrician B

For Electrician B, the coefficient of $x$ in the right - hand side of the inequality is the hourly rate and the constant is the flat - fee. So Electrician B charges $\$27$ per hour plus a flat fee of $\$200$.

Step3: Analyze the variable $x$

$x$ represents the number of hours of work. Since $35x + 100<27x+200$, Electrician A's total cost would have to be less than Electrician B's total cost.

Answer:

1. Inequality: $40000x>37500x + 10000$

2.
a) $35$, $100$
b) $27$, $200$
c) number of hours of work, less than