Question 681818
{{{w}}} = percent of water (as in 60 for 60%)
{{{f}}} = percent of fat
{{{p}}} = percent of protein
"Ninety-five percent of her total body weight consists of water, fat, and protein" translates as
{{{w+f+p=95}}}
(We do nor care about her weight).
"he difference between the percentage of body weight consisting of water and fat is 35%" translates as
{{{w-f=35}}}
"The difference between the percentage of body weight consisting of fat and protein is 9%" translates as
{{{f-p=9}}}
We end up with the system
{{{system(w+f+p=95,w-f=35,w-f=35)}}}
There are many ways to solve a system of equations, but this is an easy one, and substitution (which is intuitive) works well.
{{{w-f=35}}} --> {{{w=f+35}}} and
{{{f-p=9}}} --> {{{highlight(f=p+9)}}}
Substituting that expression for {{{f}}} into {{{w=f+35}}} we get
{{{w=(p+9)+35}}} --> {{{w=p+(9+35)}}} --> {{{highlight(w=p+44)}}}
Substituting the highlighted expressions for {{{f}}} and {{{w}}} into {{{w+f+p=95}}} we get
{{{(p+44)+(p+9)+p=95}}} --> {{{(p+p+p)+(44+9)=95}}} --> {{{3p+53=95}}} --> {{{3p=95-53}}} --> {{{3p=42}}} --> {{{p=42/3}}} --> {{{highlight(p=14)}}}
Then, we substitute the value found for {{{p}}} into the expressions we had found before for {{{w}}} and {{{f}}}
{{{highlight(f=p+9)}}} --> {{{f=14+9}}} --> {{{highlight(f=23)}}}
{{{highlight(w=p+44)}}} --> {{{w=14+44}}} --> {{{highlight(w=58)}}}
The percentages of total body weight consisting of of water, fat, and protein are {{{highlight(58)}}}%, {{{highlight(23)}}}% and {{{highlight(14)}}}% respectively.