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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Bf%2Bp=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%28w%2Bf%2Bp=95%2Cw-f=35%2Cw-f=35%29
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%2B35 and
f-p=9 --> highlight%28f=p%2B9%29
Substituting that expression for f into w=f%2B35 we get
w=%28p%2B9%29%2B35 --> w=p%2B%289%2B35%29 --> highlight%28w=p%2B44%29
Substituting the highlighted expressions for f and w into w%2Bf%2Bp=95 we get
%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
Then, we substitute the value found for p into the expressions we had found before for w and f
highlight%28f=p%2B9%29 --> f=14%2B9 --> highlight%28f=23%29
highlight%28w=p%2B44%29 --> w=14%2B44 --> highlight%28w=58%29
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.