Question

A doctor reports blood pressure in millimeters of mercury (mm Hg) as a ratio of systolic blood pressure to diastolic blood pressure (such as 140 over 80). Systolic pressure is measured when the heart beats, and diastolic pressure is measured when it rests. Refer to the table of blood pressure ranges for adults.

Blood Pressure Ranges
	Normal	Prehypertension	Hypertension (Very High)
Systolic	Under 120 mm Hg	120-139 mm Hg	140 mm Hg and above
Diastolic	Under 80 mm Hg	80-89 mm Hg	90 mm Hg and above

Manohar is a healthy 37 years old man whose blood pressure is in the normal category.

1. Calculate an approximate ratio of systolic to diastolic blood pressures in the normal range.
2. If Manohar’s systolic blood pressure is 102 mm Hg, use the ratio from part (a) to predict his diastolic blood pressure.
3. Calculate the ratio of average systolic to average diastolic blood pressure in the prehypertension category.

Answer 1

a. Systolic blood pressure in the normal range = 120 mm Hg

Diastolic blood pressure in the normal range = 80 mm Hg

The approximate ratio of systolic to diastolic blood pressure

= `"Systolic blood pressure in normal range"/"Diastolic blood pressure in the normal range"`

= `120/80`  .....[Dividing numerator and denominator by 40]

= `3/2`  

Hence, the approximate ratio is 3:2.

b. Manohar's systolic blood pressure = 102 mm Hg

Let diastolic blood pressure = x mm Hg

According to the question,

`"Systolic blood pressure"/"Diastolic blood pressure" = 3/2`  ......[From part (a)]

⇒ `102/x = 3/2`

⇒ x = `(102 xx 2)/3`

∴ x = 68 mm Hg

Hence, Manohar's diastolic blood pressure is 68 mm Hg.

c. Average systolic blood pressure in the prehypertension category

= `(120 + 139)/2`

= `259/2` mm Hg

Average diastolic blood pressure in prehypertension category

= `(80 + 89)/2`

= `169/2` mm Hg

Hence, the ratio of average systolic to average diastolic blood pressure

= `"Average systolic blood pressure"/"Average diastolic blood pressure"`

= `(259/2)/(169/2) xx 259/2 xx 2/169`

= `259/169`

Hence, the required ratio is 259:169.