Question 715577
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
{{{14/17}}} , so the total number of right handed students is
{{{714(14/17)=highlight(588)}}}
 
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
{{{3/14=(714-x)/x}}}
"Equating the cross products"
or multiplying both sides of the equal sign times {{x}}} and times {{{14}}} we get
{{{3x=(714-x)*14}}}
{{{3x=9996-14x}}}
{{{3x+14x=9996}}}
{{{17x=9996}}}
{{{x=9996/17}}}
{{{highlight(x=588)}}}
 
AND ANOTHER WAY:
The ratio of left-handed to right-handed students is
{{{3/14=3y/14y}}}
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+14y=17y}}} .
So {{{17y=714}}} --> {{{y=714/14}}} --> {{{y=42}}}
and the number of right-handed students is
{{{14y=14*42}}} --> {{{14y=highlight(588)}}}