Question

Suppose that of the 143 patients who visited Doctor Baptiste's office this week, 41 had high LDL cholesterol, 32 had hypertension, and 88 had neither high LDL cholesterol nor hypertension. Let C be the number of patients with high LDL cholesterol and H the number with hypertension. How many patients had both high LDL cholesterol and hypertension, │ C ∩ H│?

C ∩ H =

Answer 1

To find the number of patients with both high LDL cholesterol and hypertension, we subtract the number of patients with neither from the total number of patients, and the sum of patients with high LDL cholesterol and hypertension. The number of patients with both high LDL cholesterol and hypertension is 18.

Step-by-step explanation:

To find the number of patients who had both high LDL cholesterol and hypertension, we need to subtract the number of patients who had neither from the total number of patients and the sum of patients with high LDL cholesterol and hypertension. Let's denote C as the number of patients with high LDL cholesterol and H as the number of patients with hypertension.

We are given that 143 patients visited the office this week, out of which 88 had neither high LDL cholesterol nor hypertension. This means that the total number of patients who had either high LDL cholesterol, hypertension, or both is 143 - 88 = 55.

Out of these 55 patients, 41 had high LDL cholesterol and 32 had hypertension. To find the number of patients who had both high LDL cholesterol and hypertension (C ∩ H), we can add the number of patients with high LDL cholesterol (C) and the number of patients with hypertension (H) and subtract the total number of patients who had either (C ∪ H):

│C ∩ H│ = C + H - (C ∪ H)

So, │C ∩ H│ = 41 + 32 - 55 = 18.