SOLUTION: 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

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.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= percent of water (as in 60 for 60%)
= percent of fat
= percent of protein
"Ninety-five percent of her total body weight consists of water, fat, and protein" translates as

(We do nor care about her weight).
"he difference between the percentage of body weight consisting of water and fat is 35%" translates as

"The difference between the percentage of body weight consisting of fat and protein is 9%" translates as

We end up with the system

There are many ways to solve a system of equations, but this is an easy one, and substitution (which is intuitive) works well.
--> and
-->
Substituting that expression for into we get
--> -->
Substituting the highlighted expressions for and into we get
--> --> --> --> --> -->
Then, we substitute the value found for into the expressions we had found before for and
--> -->
--> -->
The percentages of total body weight consisting of of water, fat, and protein are %, % and % respectively.
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