algebra 1/2 question

Question

 

In a math course, a student scored 100 on one test,97 on another test, and 88 on each of the other tests. The students test average, where each is weighted equally is exactly 91. What is the total number of math tests that student has taken in the course?

 

 

A) 3

B) 5

C)7

D)15

E)Cannot be determined

 

 

PLEASE HELP. I know how to take averages but I am obivously doing/missing something. I would really appreciate any help. Please try to show all work. THANK YOU!!!

Answer 1

The problem asks us to find N = the total number of math tests taken.
The problem gives the formula:
     Average = 91 = (100 + 97 + (N-2)*88) / N
    91N = 197 + (N-2)*88         [multiply both sides by N and collect terms]
    91N = 197 + 88N - 176       [distribute 88)
      3N = 21        [subtract 88N from both sides]
       N = 7             [divide both sides by 3]

Check:
     Is 97 = (100 + 97 + 5*88)/7   ?
         97 = 637/7  ?     yes

Answer 2

This did take me a several minutes to figure out :)

• You took 2 tests first, then an unknown amount of tests...let call that unknown n
• Every remaining test you got the same score of 88
• Scores from all tests ÷ total no. of tests = average score

 

[100+97+(88 • unknown amt of tests)] ÷ (2 original tests +unknown amt of tests) = 91

 

(197 + 88n)÷(2 + n )= 91

 

197 + 88n = 91(2 + n) ...(multiplying both sides by 2+n)

 

197 + 88n = 182 + 91n

 

197 = 182 + 3n  .....(Subtracting 88n from both sides)

 

15 = 3n ....(subtracting 182 from both sides)

 

n = 5 ...(dividing both sides by 3)

 

so if we add the 5 new tests to our original 2 tests, we get 7 TESTS TOTAL