Body Mass Index
MAT221 Introduction to Algebra
Instructor Pamela Clarke
November 17, 2013
I am going to solve the following 4 formulas involving Body Mass Index starting with the first one. 17<703WH^2<22 This is the equivalent inequality where I substituted BMI with the formula. Then I replace the H^2 with my height in inches. 17<703W73^2<22 After factoring in my height to the second power I get 17<703W5329<22 Now I multiply all 3 terms by the denominator 17(5329) < 703W(5329)5329 <22(5329) and then get 90593 < W < 117238. Then finally I divide all 3 by 703 in order to isolate W. 128.8 < W < 166.7 So people with the height of 73 inches could have a longer than average life span if they weigh between 129 and 167 pounds.
The next equation 23<703WH^2<25 I first multiply all 3 terms by H^2 in order to take our the denominator. 23H^2 < 703W < 25H^2 Then I divide all terms by 703 to isolate the W. 23H^2703<W< 25H^2703 After doing this it now becomes an equivalent inequality for me to solve the second weight. I now use my height squared to find the second weight interval. 23(5329)703<W< 25(5329)703 After I multiply I end up with 122567703<W< 133225703 Then I simply divide and end up with 174 < W < 189.5. So people who are 73 inches tall that way between 174 and 189.5 are probably not overweight.
Now for the third equation I will use 25 and 30 in place of 23 and 25 in the above equation. 25(5329)703<W< 30(5329)703 Then I will multiply the parentheses. 133225703<W< 159870703
Then I must do the division. 189.5 < W < 227. So people that are 73 inches tall and also weigh between 189.5 and 192 are overweight.
The last and final equation is. 703W73^2<30 Now I first do my power of inches which is. 703W5329<30 Now for the division which then turns into multiplication instead and we take both times the 5329 instead of division. I end up with 703W > 159870. Now to...