document.write( "Question 681818: system of equations in three variables word problem: This exercise refers to the body composition of a 135-pound adult female. Ninety-five percent of her total body weight consists of water, fat, and protein. The difference between the percentage of body weight consisting of water and fat is 35%. The difference between the percentage of body weight consisting of fat and protein is 9%. Find the percentage of total body weight consisting of of water, fat, and protein. \n" ); document.write( "

Algebra.Com's Answer #422834 by KMST(5328) $\"\"$ $\"About$

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$\"w\"$ = percent of water (as in 60 for 60%)
\n" ); document.write( " $\"f\"$ = percent of fat
\n" ); document.write( " $\"p\"$ = percent of protein
\n" ); document.write( "\"Ninety-five percent of her total body weight consists of water, fat, and protein\" translates as
\n" ); document.write( " $\"w%2Bf%2Bp=95\"$
\n" ); document.write( "(We do nor care about her weight).
\n" ); document.write( "\"he difference between the percentage of body weight consisting of water and fat is 35%\" translates as
\n" ); document.write( " $\"w-f=35\"$
\n" ); document.write( "\"The difference between the percentage of body weight consisting of fat and protein is 9%\" translates as
\n" ); document.write( " $\"f-p=9\"$
\n" ); document.write( "We end up with the system
\n" ); document.write( " $\"system%28w%2Bf%2Bp=95%2Cw-f=35%2Cw-f=35%29\"$
\n" ); document.write( "There are many ways to solve a system of equations, but this is an easy one, and substitution (which is intuitive) works well.
\n" ); document.write( " $\"w-f=35\"$ --> $\"w=f%2B35\"$ and
\n" ); document.write( " $\"f-p=9\"$ --> $\"highlight%28f=p%2B9%29\"$
\n" ); document.write( "Substituting that expression for $\"f\"$ into $\"w=f%2B35\"$ we get
\n" ); document.write( " $\"w=%28p%2B9%29%2B35\"$ --> $\"w=p%2B%289%2B35%29\"$ --> $\"highlight%28w=p%2B44%29\"$
\n" ); document.write( "Substituting the highlighted expressions for $\"f\"$ and $\"w\"$ into $\"w%2Bf%2Bp=95\"$ we get
\n" ); document.write( " $\"%28p%2B44%29%2B%28p%2B9%29%2Bp=95\"$ --> $\"%28p%2Bp%2Bp%29%2B%2844%2B9%29=95\"$ --> $\"3p%2B53=95\"$ --> $\"3p=95-53\"$ --> $\"3p=42\"$ --> $\"p=42%2F3\"$ --> $\"highlight%28p=14%29\"$
\n" ); document.write( "Then, we substitute the value found for $\"p\"$ into the expressions we had found before for $\"w\"$ and $\"f\"$
\n" ); document.write( " $\"highlight%28f=p%2B9%29\"$ --> $\"f=14%2B9\"$ --> $\"highlight%28f=23%29\"$
\n" ); document.write( " $\"highlight%28w=p%2B44%29\"$ --> $\"w=14%2B44\"$ --> $\"highlight%28w=58%29\"$
\n" ); document.write( "The percentages of total body weight consisting of of water, fat, and protein are $\"highlight%2858%29\"$ %, $\"highlight%2823%29\"$ % and $\"highlight%2814%29\"$ % respectively. \n" ); document.write( "

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