Question

1. the number of patients in the hospital has increased from 160 to 200. what is the percent of change?
2. a patient weighed 400 pounds before a diet program. after the program she weighed 280 pounds. what was the percent of change in the patient’s weight?

Explanation:

Question 39

Step1: Find the change in number

First, we find the amount of change. The initial number of patients is 160 and the final number is 200. So the change is \( 200 - 160 = 40 \).

Step2: Calculate percent change

The formula for percent change is \( \text{Percent Change} = \frac{\text{Change}}{\text{Original Amount}} \times 100\% \). Here, the original amount is 160 and the change is 40. So we substitute these values into the formula: \( \frac{40}{160} \times 100\% \).
Simplify \( \frac{40}{160} = \frac{1}{4} \), and \( \frac{1}{4} \times 100\% = 25\% \).

Step1: Find the change in weight

First, find the amount of weight change. The initial weight is 400 pounds and the final weight is 280 pounds. So the change is \( 400 - 280 = 120 \) pounds.

Step2: Calculate percent change

Using the percent change formula \( \text{Percent Change} = \frac{\text{Change}}{\text{Original Amount}} \times 100\% \). The original amount is 400 and the change is 120. Substitute these values: \( \frac{120}{400} \times 100\% \).
Simplify \( \frac{120}{400} = \frac{3}{10} \), and \( \frac{3}{10} \times 100\% = 30\% \). Since the weight decreased, it is a 30% decrease.

Answer:

The percent of change is \( 25\% \).

Question 40