Question
upstudy study bank question image url

A student scored 69 points on his Psychology 101 midterm. If the average of his midterm and final must be between 78 and 90 inclusive for a B, then for what range of scores on the final exam would a student get a B? Both tests have a maximum of 100 points. Hint: Write a compound inequality-with his average between 78 and 90 inclusive.

Ask by Ryan Guerrero. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

To get a B, the student needs to score between 87 and 100 on the final exam.

Solution

To determine the range of final exam scores that would result in a **B** for the student, we'll follow these steps: 1. **Understand the Requirements:** - **Midterm Score:** 69 points - **Final Exam:** Maximum of 100 points - **Average Needed for a B:** Between 78 and 90 (inclusive) 2. **Set Up the Compound Inequality:** The average of the midterm and final exam scores should be between 78 and 90. This can be expressed as: \[ 78 \leq \frac{\text{Midterm} + \text{Final}}{2} \leq 90 \] 3. **Plug in the Midterm Score:** \[ 78 \leq \frac{69 + \text{Final}}{2} \leq 90 \] 4. **Multiply All Parts by 2 to Eliminate the Fraction:** \[ 156 \leq 69 + \text{Final} \leq 180 \] 5. **Subtract 69 from All Parts to Solve for the Final Exam Score:** \[ 87 \leq \text{Final} \leq 111 \] 6. **Consider the Maximum Possible Score:** Since the final exam is out of 100 points, the upper limit of 111 is not possible. Therefore, the final exam score must be **no more than 100**. 7. **Final Range:** \[ 87 \leq \text{Final} \leq 100 \] **Conclusion:** To achieve a **B**, the student must score **at least 87** points on the final exam and **no more than 100** points. **Answer:** All final exam scores from 87 through 100 are eligible for a B.

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

Bonus Knowledge

To find the range of scores needed on the final exam, we first calculate the total score required for both the lower and upper bounds of the average. For an average of 78: \[(69 + F)/2 \geq 78\] \[69 + F \geq 156\] \[F \geq 87\] For an average of 90: \[(69 + F)/2 \leq 90\] \[69 + F \leq 180\] \[F \leq 111\] Since the final exam can only be a maximum of 100 points, we then limit our upper bound to 100. Thus, the range of final exam scores needed for a B is: \[87 \leq F \leq 100.\] This means the student must score between 87 and 100 points on the final exam for a B!

Latest Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy