A student in algebra course has test scores of 78, 83, 74, and 82. What score on the next test will raise the student's average to 80?

Question

A student in algebra course has test scores of 78, 83, 74, and 82. What score on the next text will raise the student's average to 80?

Answer 1

using algebra...

(78+83+74+82+n)/5=80

(78+83+74+82+n)=5(80)

n+317=400

n=400-317

n=83 for the next test score

 

using arithmetic...

having an 80 average on 5 tests is the same has having all 5 test scores be 80

rearranging the scores we have 78, 82, 83, and 74

take 2 points from 82 and add them to 78 to get 82-2=80 and 78+2=80

now we have 80, 80, 83 and 74

take 3 points from 83 and add them to 74 to get 83-3=80 and 74+3=77

now we have 80, 80, 80, and 77

we need 5 80s to have an 80 average, but 77 is 3 points short

on the next test we need to get 80+3 points, or 83 points because we need the 80 for the 80 average plus the 3 points that the 77 is short

Answer 2

The student's scores so far add up to 78+83+74+82 = 317

 

An average score of 80 over 5 tests adds up to 80+80+80+80+80 = 80*5 = 400

 

400 - 317 = 83

 

The student needs a score of 83.