A person weighed themselves at 160 lb. Three months later they weighed themselves at 130 lb. Which of the following is the percent of weight the person lost over 3 months? (Round to the nearest percent.)
A.
20%
B.
13%
C.
19%
D.
29%
The Correct answer and Explanation is:
To find the percent of weight loss, we need to use the following formula:Percent Change=(Original Weight−New WeightOriginal Weight)×100\text{Percent Change} = \left(\frac{\text{Original Weight} – \text{New Weight}}{\text{Original Weight}}\right) \times 100Percent Change=(Original WeightOriginal Weight−New Weight)×100
Given:
- Original weight = 160 lb
- New weight = 130 lb
Step 1: Calculate the difference in weight.Weight Loss=160 lb−130 lb=30 lb\text{Weight Loss} = 160 \text{ lb} – 130 \text{ lb} = 30 \text{ lb}Weight Loss=160 lb−130 lb=30 lb
Step 2: Divide the weight loss by the original weight.30 lb160 lb=0.1875\frac{30 \text{ lb}}{160 \text{ lb}} = 0.1875160 lb30 lb=0.1875
Step 3: Convert the decimal to a percentage.0.1875×100=18.75%0.1875 \times 100 = 18.75\%0.1875×100=18.75%
Step 4: Round the percentage to the nearest whole number.18.75%≈19%18.75\% \approx 19\%18.75%≈19%
Thus, the correct answer is:
C. 19%
Detailed Explanation:
When calculating the percentage of weight loss, the key is to determine how much weight was lost relative to the original weight. The formula used is a standard percentage change calculation, which measures the difference between the original and new values, divided by the original value, and then multiplied by 100 to convert it into a percentage.
In this case, the individual lost 30 pounds over three months. Dividing this weight loss by the original 160 pounds gives a proportion of 0.1875, which represents the fraction of the original weight that was lost. When converting this fraction to a percentage, we multiply by 100, resulting in 18.75%. Since percentages are typically rounded to the nearest whole number, we round 18.75% to 19%.
This 19% weight loss is significant and indicates that the person experienced a substantial decrease in body weight. Weight loss of this magnitude could be intentional, possibly due to a structured diet and exercise program, or it could be unintentional, requiring medical evaluation. It’s essential to recognize and understand the context in which weight changes occur, as this can impact overall health and well-being.