Question

A doctor uses the formula in the box to calculate a patient's body mass index (BMI).A patient is described as underweight if their BMI is below 18.5.
a) Tina’s mass is 48.8kg and her height is 1.56m.Is she underweight? Explain your answer.
b) Stephen’s height is 1.80m and his mass is 68.5kg. He wants to have a BMI of 20.How many kilograms must he lose to reach a BMI of 20? Show your working.
Formula used by doctors for BMI= \[\dfrac{m}{{{h^2}}}\] where m is the mass in kilograms and h is the height in meters.

Answer 1

Hint:First we will use the doctor’s formula to calculate the BMI of Tina and compare it with 18.5,if it is greater than 18.5 then Tina is not underweight and otherwise she is underweight.
Next we will similarly calculate the BMR of Stephen and get the required answer.

Complete step-by-step answer:
Given that, formula used by doctor for BMI= \[\dfrac{m}{{{h^2}}}\] where m is the mass in kilograms and h is the height in meters.
a) Tina’s mass is 48.8kg and her height is 1.56m.
Here, \[m = 48.8kg,h = 1.56m\]
Thus Tina’s BMR calculated by the formula used by doctor is
\[ = \dfrac{{48.8}}{{{{(1.56)}^2}}}\]
By calculating square in the denominator we get,
\[ = \dfrac{{48.8}}{{2.4336}}\]
Tina's BMI\[ = 20.05kg/{m^2}\]
Given that, a patient is described as underweight if their BMI is below 18.5.
Since, 20.05>18.5, Tina is not underweight.
b) Given that, Stephen’s height is 1.80m and his mass is 68.5kg.
Here,\[m = 68.5kg,h = 1.80m\]
Thus Stephen’s BMR calculated by the formula used by doctor is
\[ = \dfrac{{68.5}}{{{{(1.80)}^2}}}\]
By calculating the square in the denominator we get,
\[ = \dfrac{{68.5}}{{3.24}}\]
Stephen’s BMI\[ = 21.14kg/{m^2}\]
So it is greater than 20,
Let, he must lose \[x\] kg weight to reach a BMI of 20.
Then,
\[\dfrac{{68.5 - x}}{{{{(1.80)}^2}}} = 20\]
By calculating the square in the denominator we get,
\[\dfrac{{68.5 - x}}{{3.24}} = 20\]
By cross multiplying the term in the denominator we get,
\[68.5 - x = 64.8\]
Let us calculate further to find the weight he must loss,
\[x = 68.5 - 64.8\]
\[x = 3.7kg\]
Hence, he must lose 3.7kg weight to reach a BMI of 20.

Note:
Formula used by doctors for BMI= \[\dfrac{m}{{{h^2}}}\] where m is the mass in kilograms and h is the height in meters. It is known that BMI 20 is considered as the correct BMI for any person whereas below 18.5 is considered as the underweight.