Question

Raphael’s test grades in a class with four tests are, so far, 65, 70, and
82. He has not yet taken the fourth test. The average of the tests counts
as 60% of his overall grade. His homework average, that counts 40% of
the grade, is 100. Set up an equation, the solution to which would be the
grade Raphael needs on the fourth test to earn an course grade of 80%.
Then, show how to solve the equation.

Answer 1

Given : Raphael’s test grades in a class with four tests are, so far, 65, 70, and  82. He has not yet taken the fourth test. The average of the tests counts  as 60% of his overall grade. His homework average, that counts 40% of  the grade, is 100.

To Find  :  grade Raphael needs on the fourth test to earn an course grade of 80%.

Solution:

Question data is not complete as maximum marks are not mentioned

Assuming that   tests  are 100 marks Each

homework  25 each    

Total Marks  =  4 * ( (60/100)100 + (40/100)25)  =  280

80 % of 280  =  224

224 Marks required

M = Marks in fourth test.

Marks  =  ( 65 + 70 + 82 + M ) * (60/100) +  (40/100)100  

=> (217 + M ) 0.6  + 40  = 224

=> 217 + M = 306.67

=> M = 89,67

He need 90 marks in fourth test

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