Question

Please help!

The guidelines for a healthy adult are to maintain a Body Mass Index (BMI) between 19.5 and 24.9. A formula that relates the height of an adult to his or her weight and BMI is shown in the picture below, where h=height in inches, w=weight in pounds, and M=BMI.

1.) Find the formula that will directly calculate BMI given a person's height and weight.

2.) Chris weighs 211 pounds and has a BMI of 28.5. How many whole pounds must he gain or lose to get into the healthy BMI range?

Thank you!!

Answer 1

To answer the first problem you are going to need to solve the equation for M (BMI). In order to do this you need to rearrange the variables h and w to one side of the equation, and M by itself on the other side. After doing this your equation should look like:
M = (0.45*w) / ((h / 40)^2)

For part 2 we must first solve for Chris' height so that we can find his healthy range. You should use the original equation for this. You should get 73.0105 inches as an answer. Now we must solve for his weight using 24.9 as the upper limit of the healthy BMI range as well as his height. You need a new formula solving for w. I am not going to put this formula here but I will just solve for W.
His healthy weight in pounds turns out to be 184.348 pounds. In order to get into this range, he must lose 211 - 184.348 = 26.6524 pounds. Since it asks how many whole pounds he must lose you should put 27 pounds as your answer.
Hope this helped!

Answer 2

1.
`h=40\sqrt{(.45w)/(M)}\Rightarrow(h^2)/(1600)=\frac{.45w}M\Rightarrow M=(720w)/(h^2)`

2. his BMI has to be reduced by 28.5-24.9=3.6

We must thus solve
`(720w)/(h^2)=3.6` thus
`(720w)/(h^2)=3.6h^2/720=.005h^2`. We can know his height using the first formula :
`h=40\sqrt{(.45w)/(M)}=40\sqrt{(.45*211)/(28.5)}\approx73.01`

Hence he must lose
`(73.01)^2*.005\approx26.6` -> 27 pounds.

We check our result :
`720*(211-27)/(73.01^2)\approx24.85<24.9`