Help with algebra word problem

Question

A student has received 56, 70, 61 and 46 on his first four college algebra exams this semester. He asked the instructor what grade he would need to make on the fifth exam to pass the course. What score will he need to earn to receive 70% or higher on the fifth exam? Set up an equation/inequality and show all work and find the solution.

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to set up an algebraic expression that represents the information given in the question. On this one we have

(56 + 70 + 61 + 46 + x) / 5  >=  70      because the average score across the 5 exams needs to be higher than 70

From there then you can solve for the value of x algebraically!

(56 + 70 + 61 + 46 + x) >= 350

233 + x >= 350

x >= 117

so unless there is a lot of bonus point/extra credit opportunity on the final it’s going to be impossible for the student to end up passing the course

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

You want the average of all 5 exams to be at least 70.

 

x = score on 5th exam

 

(56 + 70 + 61 + 46 + x)/5 ≥ 70

 

Solve for x.  The result is

 

x ≥ 117, which is an impossible score, so the student cannot pass.