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MA.912.A.3.5 Real-World Application of Multi-Step Equations

What You Need To Know...

Solve linear equations and inequalities.

  1. The benchmark will assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. Items may require students to express inequalities on a number line, or to use an inequality for a response.
  3. Items may require students to interpret a real-world application and write and/or solve a multi-step linear equation or linear inequality.
  4. Items may include compound inequalities presented in written format, graphically, and/or algebraically. 

Example One

The out-of-pocket costs to an employee for health insurance and medical expenses for one year are shown in the table below.


Type of Cost Definition Cost to Employee
Premium Total amount employee pays insurance company for the policy  $3,626
Deductible Amount of medical expenses employee pays before insurance company pays for anything $500
Co-payment Percentage of medical expenses after the first $500 that employee has to pay 20%

According to the plan outlined in the table, total annual health care costs, C, depend on the employee's medical expenses for that year. If x represents the total medical expenses of an employee on this plan and x > 500, which of the followiing equations can be used to determine the employee's total health care cost for that year?

A.  C = 3,626 –  500 + 0.20(x  500)
B.  C = 3,626   500 + 0.20x
C.  C = 3,626 + 500 + 0.20(x 500)
D.  C = 3,626 + 500 + 0.20x 



Example Two

Karen works as a salesperson for a local marketing company. Using the equations shown below, the company calculates her monthly earnings based upon her total sales for the month.


Total Sales for the Month
(s in dollars)
Earnings Equation
s < $5,000 E = 1,600 + 0.1s
s > $5,000 E = 1,600 + 0.1s + 0.15(s - 5000)


      E represents total monthly earnings before taxes and withholding
      s represents the dollar amount of her total sales 

Karen's total sales were greater than $5,000 in October.  If her total monthly earnings for October were $3,000, what was the value of her total monthly sales, s ?

Answer grid.jpg



Example Three

Ethan's job at a local home improvement store is to mix paint to make different colors.  For a particular customer, he mixed p liters of blue paint, 0.8p liters of yellow paint, and p - 0.4 liters of orange paint.  He then divided the mixture evenly into two cans.  If each can contains 1.9 liters of paint, how many liters of blue paint did he use?



Additional Examples



Word Problem Equations

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Real-World Equations

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Real-World Part 2

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Multi-Step Inequalities

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Linear Applications

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Reference Sheet