Question

The normal systolic blood pressure P, in millimeters of mercury, for an adult made x years old can be modeled by the equation $P=\dfrac{x+220}{2}$ . According to the model, for every increase of 1 year in age, by how many millimeters of mercury will the normal systolic blood pressure for an adult male increase?

Answer 1

Hint: To find the normal systolic blood pressure for an adult male increase for every increase of 1 year in age, we need to first find the systolic blood pressure by considering the present age as ‘x’. Then we will find the systolic blood pressure by increasing 1 year in the age of a man as $x+1$ . By subtracting these both, we will get millimeters of mercury and the normal systolic blood pressure for an adult male increase.

Complete step-by-step answer:
It is given in the question that –
For every increase of 1 year in age, millimeters of mercury the normal systolic blood pressure for adult male increases.
Let us consider ‘x’ as the present age and ‘x+1’ be the age of a man after 1 year
It is given in the question that the normal systolic blood pressure is $P=\dfrac{x+220}{2}$ .
Now, we will find the normal systolic blood pressure when the age of an adult man is ‘x’.
So, we get –
$P=\dfrac{x+220}{2}$
After 1 year the age of an adult man turns $x+1$ .
Then the normal systolic blood pressure be –
$\begin{align}
  & P=\dfrac{\left( x+1 \right)+220}{2} \\
 & =\dfrac{x+1+220}{2} \\
 & =\dfrac{x+221}{2} \\
\end{align}$
Therefore, the difference between the normal systolic blood pressure when the age of adult increases in $\dfrac{x+221}{2}-\dfrac{x+220}{2}$
By simplifying the above equation, we get –
$\begin{align}
  & =\dfrac{x+221-\left( x+220 \right)}{2} \\
 & =\dfrac{x+221-x-220}{2} \\
 & =\dfrac{1}{2} \\
 & =0.5 \\
\end{align}$
Hence, 0.5 millimeters of mercury will be the normal systolic blood pressure for an adult male increase.

Note: Students should be careful with parentheses, the given equation of parentheses is $P=\dfrac{(x+220)}{2}$ . while simplifying this equation they may take it as $P=x+110$ by cancelling 220 by 2 which is wrong and this may lead them to get wrong answer. We can also substitute the value of x as any number and check once, whichever be the value of x, we will get 0.5 millimeters of mercury increase in normal systolic blood pressure for an adult male every year.