SOLUTION: JOE SPENT 1/3 OF HIS STUDY TIME DOING MATH HOMEWORK AND 2/7 PREPARING FOR A HISTORY EXAM. WHAT FRACTION OF HIS STUDY TIME REMAINS?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: JOE SPENT 1/3 OF HIS STUDY TIME DOING MATH HOMEWORK AND 2/7 PREPARING FOR A HISTORY EXAM. WHAT FRACTION OF HIS STUDY TIME REMAINS?      Log On


   

Question 145873: JOE SPENT 1/3 OF HIS STUDY TIME DOING MATH HOMEWORK AND 2/7 PREPARING FOR A HISTORY EXAM. WHAT FRACTION OF HIS STUDY TIME REMAINS?
Found 2 solutions by jojo14344, aswathytony:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Let "x" = total study time
So,
%281%2F3%29x = Math homework
%282%2F7%29x= Preparing history exam
Adding the two we'll get the time allocated for these right?
=%281%2F3%29x+%2B+%282%2F7%29x
=%287x%2B6x%29%2F21
= +highlight%28%2813%2F21%29x%29 -------- time allocated for Math & history
So total study time remaining,
=x-+%2813%2F21%29x
=x%281-13%2F21%29
=highlight%28%288%2F21%29x%29 ----------- time remainig to study
So if he has total 60 minutes allocated(just an example) for the whole study,
= %288%2F21%29%2860%29
= 22.86 minutes remains
Thank you,
Jojo

Answer by aswathytony(47) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the total study time of joe.
then time used for doing math homework= 1/3 of x =1/3x
time used for preparing history exam = 2/7 of x =2/7x
let remaining time be 'y'.
then, 1/3x+2/7x+ y =x
y= x - [ 1/3x + 2/7x]
= x - [ 7x + 6x/21] Taking LCM OF 3 & 7 , AND SIMPLIFYING
= X- 13x/21
=21x -13x/21 taking LCM
= 8x/21
ie, fraction of remaining study time = 8/21