Pre-Cal Word Problem

Question

Linh has obtained scores of 86, 73, and 71 on her midterm algebra exams. If the final exam counts twice as much as a midterm, what score must she make on her final exam to get an average score of 80?

Answer 1

(86+73+71+x+x)/5=80

86+73+71+2x=400

230+2x=400

2x=400-230

2x=170

x=170/2

x=85 is what she has to get on her final exam

Answer 2

Hello Lauren,

 

Let's write the equation for unknown final score x considering that the average of 4 numbers is 80, thus the sum should be 80*4 = 320:

 

86+73+71+2x = 320

 

or in canonical form

 

2x+230=320

 

This linear equation can be easily solved either manually or using online Linear Equation Solver (http://examn8.com/LinearEquations.aspx). The solution for x:

 

x= 45 (final score)

 

Note: the problem definition can be also interpreted as it's done by Arthur D., namely that the final exam counts as two midterm exams. In this case, the number of items in average calculation would be 5 instead of 4, and correspondingly, the sum would be 80*5=400 and equation would be written as:

 

86+73+71+2x = 400

2x+230=400 resulting in x=80

 

Hope this may help.