Putting It Together: Multi-Step Linear Equations
Kristy, the college student we met earlier who was anxiously studying for her final exam, still isn't sure what grade she needs to earn to pass her math class, and the final is tomorrow! Let's put your new math skills to good use to help her figure it out. Here's what we already know:- Kristy's current grade in the class is [latex]82.3[/latex]%.
- She wants to know what score she needs on the final to keep her B in the class (>80%).
- She also wants to know what score she needs on the final to pass the class with a C (>70%).
Exam time is coming.| Homework | 150 Points |
| Quizzes | 100 Points |
| Midterm | 100 Points |
| Final Exam | 200 Points |
| TOTAL | 550 Points |
[latex]350 \times 0.823 = 288.05[/latex] points
So we know that Kristy has [latex]288.05[/latex] points. The next question to answer is: how many total points does she need to achieve a B or a C?Typically a B is 80% or .8, a C is 70% or .7
There are a total of [latex]550[/latex] points in the class. We can use this to figure out how many points Kristy would need to get a certain grade:To get a B, she needs [latex]550 \times 0.8 = 440[/latex] points.
To get a C, she needs [latex]550 \times 0.7 = 385[/latex] points.
Now we can write a linear equation to determine the number of points she needs on the final to earn either a B or a C in the class.current number of points + points needed on the final = total points needed
Again, Kristy has [latex]288.05[/latex] points. Let's call the number of points she needs on the final [latex]x[/latex]. We know that for a B, she needs [latex]440[/latex] points total. We can set up the equation and solve for [latex]x[/latex] to determine the number of points she needs on the final to earn a B.[latex]288.05+x=440[/latex]
[latex]288.05+x\color{red}{-288.05}=440\color{red}{-288.05}[/latex]
[latex]x=151.95[/latex]
To state that grade as a percentage, we can divide it by the total number of points possible on the final exam: [latex]200[/latex]. That means Kristy needs [latex]151.95/200=75.975[/latex]%. In other words, a C on the final will be enough for her to get a B in the class. Now let's calculate how many points she can earn on the final to pass the class with a C. We'll use the same equation, but this time, we'll use [latex]385[/latex] for the total number of points.[latex]288.05 + x = 385[/latex]
Solve again, and you'll find that [latex]x = 96.95[/latex]. If we divide that by [latex]200[/latex] to figure out the percentage, we learn that Kristy needs a score of [latex]48.475[/latex]% on the final to get a C in the class. In other words, she can fail the final exam and still pass. Kristy can now take the final exam knowing exactly how well she needs to do to pass the class and keep her scholarship--and it turns out that she doesn't need to be as nervous as she thought!Licenses & Attributions
CC licensed content, Original
- Putting It Together: Solving Multi-Step Linear Equations Part I. Provided by: Lumen Learning License: CC BY: Attribution.
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- Students in a classroom. Provided by: US Department of Education Located at: https://www.flickr.com/photos/departmentofed/9599973167. License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].
