SOLUTION: The ratio of left-handed to right-handed students was 3 to 14. If the total number in both categories was 714, how many were right-handed? Please help solve.

Algebra ->  Test  -> Lessons -> SOLUTION: The ratio of left-handed to right-handed students was 3 to 14. If the total number in both categories was 714, how many were right-handed? Please help solve.      Log On


   

Question 715577: The ratio of left-handed to right-handed students was 3 to 14. If the total number in both categories was 714, how many were right-handed? Please help solve.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE FIFTH GRADER SOLUTION:
If that ratio was true in a group of 17=3+14 students, you would have 3 left handed students and 14 right handed students out of 17 students.
The ratio of right handed to total would be
14%2F17 , so the total number of right handed students is
714%2814%2F17%29=highlight%28588%29

ANOTHER WAY:
x = number of right handed students
714-x = number of left handed students
The ratio of left-handed to right-handed students is
3%2F14=%28714-x%29%2Fx
"Equating the cross products"
or multiplying both sides of the equal sign times {{x}}} and times 14 we get
3x=%28714-x%29%2A14
3x=9996-14x
3x%2B14x=9996
17x=9996
x=9996%2F17
highlight%28x=588%29

AND ANOTHER WAY:
The ratio of left-handed to right-handed students is
3%2F14=3y%2F14y
If the number of left-handed students is 3y and
the number of right-handed students is 14y ,
then the total number of students is
3y%2B14y=17y .
So 17y=714 --> y=714%2F14 --> y=42
and the number of right-handed students is
14y=14%2A42 --> 14y=highlight%28588%29